Yo-Yo Ma (born October 7, 1955) is an American cellist. Born and partially raised in Paris to Chinese parents and educated in New York City, he was a child prodigy, performing from the age of four and a half. He graduated from the Juilliard School and Harvard University, attended Columbia University, and has performed as a soloist with orchestras around the world. He has recorded more than 90 albums and received 19 Grammy Awards.

In addition to recordings of the standard classical repertoire, Ma has recorded baroque music, a wide variety of folk music, such as American bluegrass music, traditional Chinese melodies, the tangos of Argentine composer Astor Piazzolla, and Brazilian music. He has also collaborated with artists from a diverse range of genres, including Bobby McFerrin, Carlos Santana, Chris Botti, Diana Krall, James Taylor, Miley Cyrus, and Sting.

Ma has been a United Nations Messenger of Peace since 2006. He has received numerous awards, including the Avery Fisher Prize in 1978, The Glenn Gould Prize in 1999, the National Medal of Arts in 2001, the Presidential Medal of Freedom in 2011, Kennedy Center Honors in 2011, the Polar Music Prize in 2012, and the Birgit Nilsson Prize in 2022. He was named as one of Times 100 Most Influential People of 2020.

Ma's primary performance instrument is the Davidov cello, made in 1712 by Antonio Stradivari.

Early life and education
Ma's mother, Marina Lu, was a singer, and his father, Hiao-Tsiun Ma, was a violinist, composer and professor of music at Nanjing National Central University (now relocated in Taoyuan, Taiwan; predecessor of the present-day Nanjing University and Southeast University). They both migrated from the Republic of China to France during the Chinese Civil War. Ma's sister, Yeou-Cheng Ma, played the violin and piano before obtaining a medical degree and becoming a pediatrician. The family moved to New York City when Ma was seven.

From the age of three, Ma played the drums, violin, piano, and later viola, but settled on the cello in 1960 at age four. When three-year-old Yo-Yo said he wanted a big instrument, his father went to see Etienne Vatelot, a foremost violin maker in Paris who, after a chat, lent him a 1/16th cello. He jokes that his first choice was the double bass due to its large size, but he compromised and took up the cello instead. When Dr. Ma realized that Yo-Yo was ready for a better teacher, a well-known cello instructor, Mme Michelle Lepinte, was selected. He began performing before audiences at age five and played for presidents Dwight D. Eisenhower and John F. Kennedy when he was seven. At age eight, he appeared on American television with his sister in an event introduced by Leonard Bernstein. In 1964, Isaac Stern introduced them on The Tonight Show Starring Johnny Carson, and they performed the Sonata of Sammartini. He attended Trinity School in New York but transferred to the Professional Children's School, where he graduated at age 15. He appeared as a soloist with the Harvard Radcliffe Orchestra in a performance of Tchaikovsky's Rococo Variations.

Ma studied at the Juilliard School at age 19 with Leonard Rose and attended Columbia University, but dropped out. He later enrolled at Harvard College. Prior to entering Harvard, Ma played in the Marlboro Festival Orchestra under the direction of cellist and conductor Pablo Casals. He spent four summers at the Marlboro Music Festival after meeting and falling in love with Mount Holyoke College sophomore and festival administrator Jill Hornor during his first summer there in 1972.

Even before that time, Ma gained fame and performed with many of the world's major orchestras. He has also played chamber music, often with pianist Emanuel Ax, with whom he has a close friendship from their days at Juilliard. Ma received his bachelor's degree in anthropology from Harvard in 1976, and in 1991 received an honorary doctorate from Harvard.

Career

In 1997, Ma was featured on John Williams' soundtrack to the Hollywood film Seven Years in Tibet. In 2000, he was heard on the soundtrack of Crouching Tiger, Hidden Dragon, and of Master and Commander: The Far Side of the World in 2003. He collaborated with Williams again on the score for the 2005 film Memoirs of a Geisha. He has also worked with Italian composer Ennio Morricone and has recorded Morricone's compositions of the Dollars Trilogy, including The Good, the Bad, and the Ugly, as well as Once Upon a Time in America, The Mission, and  The Untouchables. He has recorded over 90 albums, 19 of which are Grammy Award winners. He received the Award of Excellence from New York's International Center.

In addition to his prolific musical career, Ma collaborated in 1999 with landscape architects to design a Bach-inspired garden. Known as the Music Garden, it interprets Bach's Suite No. 1 in G Major for unaccompanied cello (BWV 1007), where the garden's sections were designed to correspond with the suite's dance movements. Toronto enthusiastically embraced the design, originally planned for Boston, and it was subsequently built in the Harbourfront neighborhood.

Ma was named Peace Ambassador by then-UN Secretary-General Kofi Annan in January 2006. He is a founding member of the influential Chinese-American Committee of 100, which addresses the concerns of Americans of Chinese heritage.

On November 3, 2009, President Barack Obama appointed Ma to serve on the President's Committee on the Arts and Humanities. His music was featured in the 2010 documentary Jews and Baseball: An American Love Story, narrated by Academy Award winner Dustin Hoffman. In 2010, President Obama announced that he would recognize Ma with the Presidential Medal of Freedom, which Ma received in February 2011.

In 2010, Ma was named Judson and Joyce Green Creative Consultant of the Chicago Symphony Orchestra. He launched the Citizen Musician initiative partnership in partnership with the orchestra's music director, Riccardo Muti. Also in 2010, he appeared on a solo album by guitarist Carlos Santana, Guitar Heaven: The Greatest Guitar Classics of All Time, playing alongside Santana and singer India Arie on a Beatles classic, While My Guitar Gently Weeps.

In 2015, Ma performed with singer-songwriter and guitarist James Taylor on three tracks of Taylor's chart-topping album Before This World: You And I Again. In 2019, Ma directed the orchestra at the annual Youth Music Culture Guangdong. Ma is represented by the independent artist management firm Opus 3 Artists. Ma contributed to the charity tribute album The Metallica Blacklist, released in September 2021, by backing Miley Cyrus on a cover of the Metallica song "Nothing Else Matters".

Silk Road Ensemble

Ma formed his own collective, the Silk Road Ensemble, named after the route across Asia which for more than 2,000  years was used for trade between Europe and China. His goal was to bring together musicians from diverse countries that were historically linked via the Silk Road. The ensemble's recordings are issued on the Sony Classical label. He also founded the Silk Road Connect, an educational pilot program for children from middle schools in the United States, including New York City.

Playing style
Yo-Yo Ma has been referred to by critics as "omnivorous" and possesses an eclectic repertoire. In addition to numerous recordings of the standard classical repertoire, he has recorded Baroque pieces using period instruments; American bluegrass music; traditional Chinese melodies, including the soundtrack to the film Crouching Tiger, Hidden Dragon; the tangos of Argentinian composer Astor Piazzolla; Brazilian music, recording traditional and contemporary songs composed by Antônio Carlos Jobim and Pixinguinha; a collaboration with Bobby McFerrin (where Ma admitted to being terrified by McFerrin's improvisation); and the music of modern minimalist Philip Glass, in such works as the 2002 Naqoyqatsi.

Ma is known for his smooth, rich tone, soulful lyricism, and virtuosity. He released a cello recording of Niccolò Paganini's Caprice No. 24 for solo violin and Zoltán Kodály's Solo Sonata.

Instruments
Ma's primary performance instrument is the Davidov cello, made in 1712 by Antonio Stradivari. It was previously owned by Jacqueline du Pré, who bequeathed it to him. Du Pré voiced her frustration with the cello's "unpredictability", but Ma attributed du Pré's sentiment to her impassioned style of playing, adding that the Stradivarius cello must be "coaxed" by the player. Prior to the Davidov, he performed on a 1722 Matteo Gofriller cello which he used for much of his early career. The instrument was previously in the possession of the French cellist Pierre Fournier.

Ma also plays on a 1733 Domenico Montagnana cello, named the "Petunia". In 2005, it was valued at US$2.5 million (US$ million in  prices). A student approached Ma after one of his classes in Salt Lake City and asked if the cello had a nickname. Ma replied, "No, but if I play for you, will you name it?" The student chose Petunia, and it stuck. In 1999, Ma inadvertently left the cello in a taxicab in New York City, but it was quickly returned undamaged. That year, when its neck was damaged during X-ray baggage inspection, he borrowed the Pawle Stradivarius cello from the Chimei Museum for a concert in Taiwan. The damage was repaired in time, but Ma played both Petunia and Pawle in the concert nonetheless.

Ma also owns a modern cello made by Peter and Wendela Moes of Warrenton, Virginia, one of carbon fiber by the Luis and Clark company of Boston, and a Samuel Zygmuntowicz cello. According to Zygmuntowicz, he "wants to give (Ma) a reason to leave his Montagnana at home."

Notable performances
 On July 5, 1986, Ma performed in the New York Philharmonic's tribute to the 100th anniversary of the Statue of Liberty, which was televised live on ABC Television. The orchestra, with conductor Zubin Mehta, performed in Central Park.

Ma performed a duet with Condoleezza Rice at the presentation of the 2001 National Medal of Arts and National Humanities Medal Awards. He was the first performer on September 11, 2002, at the site of the World Trade Center, while the first of the names of the dead were read on the first anniversary of the attack on the WTC; he played the Sarabande from Bach's Cello Suite #5 in C Minor. He performed a special arrangement of Sting's "Fragile" with Sting and the Mormon Tabernacle Choir in the opening ceremonies of the 2002 Winter Olympics in Salt Lake City, Utah. He also appeared as a Pennington Great Performers series artist with the Baton Rouge Symphony Orchestra in 2005.

He performed John Williams' "Air and Simple Gifts" at the inauguration ceremony for Barack Obama on January 20, 2009, along with Itzhak Perlman (violin), Gabriela Montero (piano), and Anthony McGill (clarinet). While the quartet played live, the music, played simultaneously over speakers and on television, was a recording made two days prior due to concerns over the cold weather damaging the instruments. Ma said, "A broken string was not an option. It was wicked cold."

On May 3, 2009, Ma performed the world premiere of Bruce Adolphe's "Self Comes to Mind" for solo cello and two percussionists with John Ferrari and Ayano Kataoka at the American Museum of Natural History in New York City. The work is based on a poetic description written for the composer of the evolution of brain into mind by neuroscientist Antonio Damasio. A film of brain scans provided by Hanna Damasio, and other images, were coordinated with the performance.

On August 29, 2009, Ma performed at the funeral mass for Senator Edward M. Kennedy. Pieces he performed included the Sarabande movement from Bach's Cello Suite No. 6 and Franck's Panis angelicus with Plácido Domingo.

On October 3, 2009, Ma appeared with Canadian prime minister Stephen Harper at the National Arts Centre gala in Ottawa. Harper, a fan of The Beatles, played the piano and sang a rendition of "With a Little Help from My Friends" while Ma accompanied him on cello. On October 16, 2011, Ma performed at the memorial of Steve Jobs at Stanford University's Memorial Church.

In 2011, Ma performed with American dancer Charles "Lil Buck" Riley in the United States and in China at the U.S.-China Forum on the Arts and Culture.

On April 18, 2013, he performed at an interfaith service to honor the victims of the Boston Marathon bombing, held at the Cathedral of the Holy Cross, where he played the Sarabande from Bach's Cello Suite No. 5 in C Minor. He and other musicians also accompanied members of the Boston Children's Chorus in a hymn.

On September 9, 2015, Ma performed all six of Bach's cello suites at the Royal Albert Hall (London) as part of the BBC Proms Season.

On September 12, 2017, Ma performed all six of Bach's cello suites at the Hollywood Bowl (Los Angeles). After the first three suites, there was a "ten-minute pause" (as the Bowl video screen described it). The audience of around 17,000 also heard him play an encore, a tribute to "cellist Pablo Casals, who as a 13-year-old in 1890 discovered an old copy of the Bach suites in a secondhand music store, bringing them to modern attention. Ma's memorable last words were, "If there are any 13-year-here—don't throw anything away."

On November 11, 2018, Ma performed at the Arc de Triomphe in Paris, with violinist Renaud Capuçon, in front of a crowd of world leaders during a ceremony marking the 100th anniversary of the end of World War I.

On May 1, 2019, he performed at Paranal Observatory in the Atacama desert. He said that his interest in astronomy motivated him to visit and perform there.

On June 20, 2019, Ma performed the Bach Complete Cello Suites in plein air at Jay Pritzker Pavilion in Chicago, Illinois. The free performance attracted what might have been his largest audience, with a pavilion capacity of 11,000, and many thousands more listening from surrounding Millennium Park.

On January 20, 2021, Ma's performance of "Amazing Grace"—pre-recorded due to the COVID-19 pandemic—was played during the inauguration of Joe Biden. In March 2021, Ma played "Ave Maria" in an impromptu waiting room concert, after receiving his second dose of a COVID-19 vaccine at Berkshire Community College in Massachusetts.

On September 14, 2021, Ma again performed Bach's six cello suites at the Hollywood Bowl, this time without intermission, pausing only briefly for applause between suites, and to announce his dedications for two of them.

Media appearances
Ma appeared as himself in an episode ("My Music Rules") of the animated children's television series Arthur, and on The West Wing (the episode "Noël"), where he played the prelude to Bach's Cello Suite No.1 at a Congressional Christmas party. He made five appearances on Sesame Street, all of which first aired during the show's 17th season in 1986. He appeared in The Simpsons episode "Puffless", where he played a serenade and theme music. Ma's likeness appeared in another Simpsons episode, "Missionary: Impossible", but he was played by regular Simpsons cast member Hank Azaria rather than Ma himself. Ma appeared twice on Mister Rogers' Neighborhood, developed a friendship with creator and host Fred Rogers, and later received the inaugural Fred Rogers Legacy Award.

He also starred in the visual accompaniment to his recordings of Bach's Six Suites for Unaccompanied Cello.

Ma was often invited to press events by Apple Inc. and Pixar CEO Steve Jobs, performed during the company's major events, and appeared in a commercial for the Macintosh computer. Ma's Bach recordings were used in a memorial video released by Apple on the first anniversary of Jobs's death.

Ma was a guest on the "Not My Job" segment of Wait Wait... Don't Tell Me! on April 7, 2007, where he won for listener Thad Moore.

On October 27, 2008, Ma appeared as a guest and performer on The Colbert Report. He was also one of the show's guests on November 1, 2011, where he performed songs from the album The Goat Rodeo Sessions with musicians Stuart Duncan, Edgar Meyer and Chris Thile. He also performed several of Bach's cello suites for the 2012 film Bill W. On October 5, 2015, he appeared on Colbert's new program, The Late Show with Stephen Colbert, in support of ballerina Misty Copeland, and prematurely celebrating his 60th birthday.

In August 2018, Ma appeared on NPR's Tiny Desk Concerts.

On June 19, 2020, the same group of musicians who recorded The Goat Rodeo Sessions released a second album, Not Our First Goat Rodeo.

On September 1, 2020, the same group performed a virtual concert of some songs from Not Our First Goat Rodeo on NPR's Tiny Desk Concerts.

On June 13, 2021, Ma was the guest on BBC Radio 4's Desert Island Discs. His musical choices included "Tin Tin Deo" by the Oscar Peterson Trio and "Podmoskovnye Vechera - Moscow Nights" by Vasily Solovyov-Sedoi. He selected as his book the 24 volumes of the Encyclopædia Britannica, and as his luxury item a Swiss Army knife. He revealed that his career in music felt like a "gift" after scoliosis threatened his ability to play in his 20s.

In 2022, Ma made a cameo appearance as himself in the Netflix film, Glass Onion: A Knives Out Mystery.

Personal life
Since 1978, Ma has been married to Jill Hornor, an arts consultant. They have two children, Nicholas and Emily. Although he personally considers it the "worst epithet he's ever faced", he was "tagged" in 2001 as "Sexiest Classical Musician" by People. He has continued to receive such accolades over the years, including from AARP in 2012. He has also been praised as a person of unquestionable character, and singled out for his humble spirit, self-effacing manner, and humanitarianism.

According to research presented by Henry Louis Gates Jr. for the PBS series Faces of America, a relative hid the Ma family genealogy in his home in China to save it from destruction during the Cultural Revolution. Ma's paternal ancestry can be traced back 18 generations to the year 1217. The genealogy was compiled in the 18th century by an ancestor, tracing everyone with the surname Ma, through the paternal line, back to one common ancestor in the 3rd century BC. Ma's generation name, Yo, was decided by his fourth great grand-uncle, Ma Ji Cang, in 1755. DNA research revealed that Ma is distantly related to actress Eva Longoria.

Aside from English, Ma is fluent in Mandarin Chinese and French.

Discography

Ma's albums include recordings of cello concertos, sonatas for cello and piano, works for solo cello, and a variety of chamber music. He has also recorded in non-classical styles, notably in collaboration with artists such as Bobby McFerrin, Carlos Santana, Chris Botti, Chris Thile, Diana Krall, James Taylor, Miley Cyrus and Sting.

Awards and recognition
Grammy Award
Grammy Award for Best Chamber Music Performance:
1986: Brahms: Cello and Piano Sonatas in E Minor Op. 38, and F Op. 99
1987: Beethoven: Cello and Piano Sonata No. 4 in C & Variations
1992: Brahms: Piano Quartets Op. 25, Op. 26
1993: Brahms: Sonatas for Cello & Piano
1996: Brahms/Beethoven/Mozart: Clarinet Trios
Grammy Award for Best Instrumental Soloist(s) Performance:
1990: Barber: Cello Concerto, Op. 22/Britten: Symphony for Cello and Orchestra, Op. 68
1993: Prokofiev: Sinfonia Concertante/Tchaikovsky: Variations on a Rococo Theme
1995: The New York Album – Works of Albert, Bartók & Bloch
1998: Yo-Yo Ma Premieres – Danielpour, Kirchner, Rouse
Grammy Award for Best Instrumental Soloist Performance:
1985: Bach: The Unaccompanied Cello Suites
Grammy Award for Best Classical Contemporary Composition:
1995: The New York Album, Stephen Albert: Cello Concerto
Grammy Award for Best Classical Album:
1998: Yo-Yo Ma Premieres – Danielpour, Kirchner, Rouse
Grammy Award for Best Classical Crossover Album:
1999: Soul of the Tango – The Music of Astor Piazzolla
2001: Appalachian Journey
2004: Obrigado Brazil
2009: Songs of Joy & Peace
Grammy Award for Best Folk Album:
2012: The Goat Rodeo Sessions w/ Stuart Duncan, Edgar Meyer & Chris Thile
Grammy Award for Best World Music Album:
2017: Sing Me Home – Yo-Yo Ma & The Silk Road Ensemble
Grammy Award for Best Chamber Music/Small Ensemble Performance:
2022: Beethoven: Cello Sonatas - Hope and Tears – Yo-Yo Ma & Emanuel Ax

Honorary doctorates

 1991: Honorary Doctor of Music, Harvard University
 2005: Honorary Doctor of Musical Arts, Princeton University
 2019: Honorary Doctor of Music, University of Oxford
2019: Honorary Doctor of Arts, Dartmouth College
2022: Honorary Doctor of Music, Stony Brook University
2022: Honorary Doctor of Music, Columbia University
Others
1978: Avery Fisher Prize
1993: Member of the American Academy of Arts and Sciences
1999: The Glenn Gould Prize
1999: Member of the American Philosophical Society
2001: National Medal of Arts
2004: Harvard Arts Medal
2004: Latin Grammy for Best Instrumental Album at the Latin Grammy Awards for Obrigado Brazil
2006: Dan David Prize
2006: Léonie Sonning Music Prize
2011: Kennedy Center Honor
2011: Presidential Medal of Freedom
2012: Polar Music Prize
2012: Songlines Music Awards - Best Cross-Cultural Collaboration for The Goat Rodeo Sessions
2013: Gramophone Hall of Fame inductee
2013: Vilcek Prize in Contemporary Music
2014: Fred Rogers Legacy Award - Inaugural Recipient. Upon reception of the award, Ma stated, "This is perhaps the greatest honor I've ever received."
2016: Commander of the Order of Arts and Letters
2020: Asia Game Changer Award from the Asia Society
2021: Praemium Imperiale
2022: Birgit Nilsson Prize

Notes

References

External links

 Yo-Yo Ma at Sony Classical
 Yo-Yo Ma's gear at Gearboard

 . Duration: 8 min 01 sec. Yo-Yo Ma, violoncello, and his sister Yeou-Cheng Ma, piano, perform the First movement of Concertino No. 3 in A major by Jean-Baptiste Bréval (1753-1823) on 29 November 1962. Kennedy Center for the Performing Arts. Retrieved April 10, 2023.

  Entry: CD04 While My Guitar Gently Weeps, Featuring – India.Arie, Yo-Yo Ma.

1955 births
20th-century American male musicians
20th-century American musicians
20th-century cellists
21st-century American male musicians
21st-century American musicians
21st-century cellists
American classical cellists
American classical musicians of Chinese descent
Asia Game Changer Award winners
Canadian Screen Award winners
Child classical musicians
Columbia University alumni
Commandeurs of the Ordre des Arts et des Lettres
Contemporary classical music performers
Fellows of the American Academy of Arts and Sciences
French emigrants to the United States
French people of Chinese descent
Glenn Gould Prize winners
Grammy Award winners
Harvard College alumni
Honorary Members of the Royal Academy of Music
Juilliard School alumni
Latin Grammy Award winners
Living people
Members of Committee of 100
Members of the American Philosophical Society
Musicians from Cambridge, Massachusetts
Musicians from New York City
Musicians from Paris
PBS people
People from Belmont, Massachusetts
Presidential Medal of Freedom recipients
Recipients of the Léonie Sonning Music Prize
Sony Classical Records artists
United Nations Messengers of Peace
United States National Medal of Arts recipients
Kennedy Center honorees

Yo-Yo Ma


Rotating bolt is a method of locking used in firearms. Johann Nicolaus von Dreyse developed the first rotating bolt firearm, the "Dreyse needle gun" in 1836. The Dreyse locked using the bolt handle rather than lugs on the bolt head like the Mauser M 98 or M16. The first rotating bolt rifle with two lugs on the bolt head was the Lebel Model 1886 rifle. The concept has been implemented on most firearms chambered for high powered cartridges since the 20th century.

Examples
 M1 Garand, gas-operated semi-automatic rifle
 Lebel Model 1886 rifle, bolt-action rifle
 Steyr-Mannlicher M1895, a straight-pull rifle
 M16, a gas-operated assault rifle
 AK-47, a gas-operated assault rifle
 IMI Tavor, a gas-operated assault rifle
 Ruger Mini-14, a gas-operated semi-automatic rifle
 IMI Desert Eagle, one of the few handguns with such mechanism.
 Remington Model 8, a recoil-operated rifle
 Chauchat, a recoil-operated light machine gun
 Remington Model 7600, a pump-action rifle
 The Winchester model 1200, 1300,and Super-X (SXP) Pump Shotguns
 SIG-Sauer MPX, the first submachine gun to use this mechanism.

References

 Primer actuated M16 bolt

Firearms

Rotating bolt


KLPS-LP was a low-power television station in the Coachella Valley, California (or the Palm Springs-Indio Nielsen ratings television market), broadcasting locally over-the-air in analog on UHF channel 19. The station has been silent since April 17, 2008, since being acquired by SMG Media Group, as the new owners needed to relocate the transmitter and main studio. The Special Temporary Authorization (STA) from the FCC was valid until October 17, 2008.

History
The station began as K19DH with an original construction permit granted to Communications Programming Agency, Inc., on March 4, 1997, but shortly thereafter, was sold to Desert Broadcasting, Inc., who completed construction and brought the station on air in late 1998. It was licensed by the FCC on January 25, 1999. Desert Broadcasting was sold to Methuselah Media, Inc., on April 16, 1999, then to a group headed by Fred Donaldson on May 1, 2001, and was renamed Desert Springs, Inc., in 2005. The station was a FamilyNet affiliate and its main studio facilities were located at a church.  On March 31, 2008, SMG Media Group acquired the station and changed its call sign to KLPS-LP.  Shortly thereafter, the new owners took the station silent so that they could relocate the main studio and transmitter. The station was run and operated digitally online (IPTV) by PNN Media Group out of Palm Springs, California. In January 2019, Pharmative, LLC purchased PNN Media group. Pharmative, LLC provides healthcare education and information on a social media platform. Dr. James Partyka, Oncology Research Scientist and Clinical Pharmacist is the owner of Pharmative, LLC along with co-owner Jimmy Mann located in Palm Springs, California.

KLPS-LP's license was cancelled by the FCC on March 19, 2015, for failure to file a license renewal application. However, since 2008, KLPS-19 currently operates as an IP Streaming Radio / TV Station owned by PHARMATIVE PNN Media Group located in Palm Springs, California.

References

External links

Religious television stations in the United States
LPS-LP
Television channels and stations established in 1997
Defunct television stations in the United States
Television channels and stations disestablished in 2015
1997 establishments in California
2015 disestablishments in California
LPS-LP

KLPS-LP


A  (plural: ) is a subdivision of several towns in Italy. The word derives from  ('third') and is thus used only for towns divided into three neighborhoods. Terzieri are most commonly found in Umbria, for example in Trevi, Spello, Narni and Città della Pieve; towns divided into terzieri in other regions include Lucca in Tuscany, and Ancona and Macerata in the Marches. The medieval Lordship of Negroponte, on the island of Euboea, was also divided into three distinct rulerships, which were known as terzieri.

Other Italian towns with more than three official neighborhoods are frequently divided into analogous quartieri (4, whence the English word "quarter" to mean a neighborhood) or sestieri (6); some towns merely refer to these neighborhoods by the non-number-specific rioni. Terzieri, quartieri, sestieri, rioni, and their analogues are usually no longer administrative divisions of these towns, but historical and traditional communities, seen especially in towns' annual palio.

See also
 Circoscrizione
 Contrade
 Frazione
 Località
 Rione
Rioni of Rome
 Quartiere
 Sestiere

Subdivisions of Italy

Terziere


The term chronic subjective dizziness (CSD) is used to describe a commonly encountered type of dizziness that is not easily categorized into one of several other types, and for which the physical examination is typically normal.  Patients with CSD frequently initially suffer a sudden injury of some sort to their vestibular system, the neurologic network that preserves sense of balance. Even after this initial injury has healed, people with CSD usually describe a vague sense of unsteadiness worsened by triggers in their environment such as high places, standing on moving objects, or standing in motion-rich environments like busy streets or crowds. There is a clear indication that anxiety and other mental illnesses play a role in the dizziness symptoms that occur with CSD. However, the condition is categorized as chronic functional vestibular disorder, not  as a structural or psychiatric condition.

Proposals include renaming it persistent postural-perceptual dizziness (PPPD) which better captures the multiple aspects of the condition under its title. It is under that title the World Health Organization has included PPPD in its draft list of diagnoses to be included to the next edition of the International Classification of Diseases (ICD-11) in 2017.

Signs and symptoms
Symptoms can include:
 A constant sense of unsteadiness, rocking or swaying, dizziness or lightheadedness
 Disequilibrium on most days for at least 3 months
 Spatial orientation problems
 Off-kilter sensation
 Extreme sensitivity to movement and/or complex visual stimuli such as grocery stores or driving in certain weather conditions
 Worsening dizziness with experience of complex visual environments such as walking through a grocery store
 Heavy-headedness; a feeling of floating, wooziness

Symptoms of CSD can be worsened by any self-precipitated motion, usually from the head, or the witnessing of motion from another subject. These are usually less noticeable when the person is lying still.

Diagnosis
Diagnosis can be difficult as there is not a specific test for PPPD but rather a series of elimination tests for other vestibular causes.  If elimination test are all normal and the symptoms match a PPPD diagnosis is possible.

Treatment
Effective treatments include vestibular rehabilitation therapy, medications such as SSRIs and psychotherapy, including the most effectively represented cognitive behavioral therapy.

Promising results were also found with transcranial direct-current stimulation combined with vestibular rehabilitation with significant improvement in symptoms of patients over a sham group in an exploratory study.

More recently, a study showed non-invasive vagus nerve stimulation to offer significant effect in PPPD patients regarding the quality of life, postural balance control, attack severity and depression level, with no reported serious side effects. The findings are argued to imply vagus nerve stimulation to be a safe and promising treatment option in patients with treatment-refractory PPPD and suggesting the need for further research.

History
Perhaps the first account of CSD was the German neurologist Karl Westphal's portrayal in the late 1800s of people who suffered dizziness, anxiety and spatial disorientation when shopping in town squares.  This phenomenon was called "agoraphobia", meaning a fear of the marketplace.  The term is now used to describe a psychological fear, but Westphal's original description included many symptoms of dizziness and imbalance not included in the modern psychiatric definition. Unlike people who feel anxious in crowds because they feel something bad will happen, people with CSD may dislike crowds because all the movement leads to a sensation of dizziness.

References

Symptoms
Neurological disorders

Chronic subjective dizziness


Nathaniel Ward (1578 – October 1652) was a Puritan clergyman and pamphleteer in England and Massachusetts.

Biography
A son of John Ward, a noted Puritan minister, he was born in Haverhill, Suffolk, England. He studied law and graduated from Emmanuel College, Cambridge University in 1603. He practised as a barrister and travelled in continental Europe. In Heidelberg he met a German Protestant reformer, David Pareus, who persuaded him to enter the ministry. In 1618 he was a chaplain to a company of English merchants at Elbing, in Poland. He returned to England and in 1628 he was appointed rector of Stondon Massey in Essex. He was soon recognised as one of the foremost Puritan ministers in Essex, and so in 1631 was reprimanded by the Bishop of London, William Laud. Although he escaped excommunication, in 1633 he was dismissed for his Puritan beliefs. (Ward's two brothers also suffered for their non-conformity.)

In 1634 Ward emigrated to Massachusetts and became a minister in Ipswich for two years. He then resigned because of ill-health. While still living in Ipswich, he wrote for the colony of Massachusetts The Body of Liberties, legal code, which was adopted by the General Court of the Massachusetts Bay Company in December 1641. This was the first code of laws established in New England. The Body of Liberties defined liberty in terms that were advanced in their day, establishing a code of fundamental principles based on Common Law, Magna Carta, and the Old Testament. However, Ward believed in theocracy rather than democracy. One of his epigrams was:

 The upper world shall Rule,
While Stars will run their race:
The nether world obey,
While People keep their place.

Ward thought that justice and the law were essential to the liberty of the individual. Some have said that The Body of Liberties began the American tradition of liberty, leading eventually to the United States Constitution.

In 1645 Ward began his second book, The Simple Cobler of Aggawam in America. This was published in England in January, 1646–1647, before Ward's return there, under the pseudonym of Theodore de la Guard. Three other editions, with important additions and changes, soon followed. The Simple Cobbler is a small book, which "in spite of its bitterness, and its lack of toleration" is "full of quaint originality, grim humor and power", according to the anthology Colonial Prose and Poetry: The Transplanting of Culture 1607–1650 (1903).

According to the anthology, the book is "probably the most interesting literary performance" in the first half of the 17th century in the English colonies that later became the United States. The book was later reprinted in 1713 and 1843 in Boston, Massachusetts.

He also wrote several religious-political pamphlets.

At the end of the English Civil War, Ward returned to England, where he wrote pamphlets, particularly Discolliminium (1650), critical of the establishment of the Commonwealth of England. His contribution to the Engagement debate (an oath of loyalty to the new Commonwealth) and his attack on polemic opponents, particularly John Dury with whom he had a 'friendly scuffle'(44), included attacking the speed with which the oath was to be administered and questioning the government's legitimacy as a just power.  Ward became the minister of the church at Shenfield in Essex and died shortly after in Shenfield.

References

External links

Cambridge History of English and American Literature – Emigrant Puritans
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1578 births
1652 deaths
17th-century American writers
17th-century English male writers
17th-century English writers
17th-century English Anglican priests
17th-century New England Puritan ministers
Alumni of Emmanuel College, Cambridge
American Christian clergy
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English Caroline nonconforming clergy
Founders of Hartford, Connecticut
Massachusetts colonial-era clergy
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Nathaniel Ward


Liberty Walther Barnes is a sociologist, ethnographer, and writer. She holds affiliations at the University of Cambridge in the United Kingdom and the University of Oregon in the United States. Trained in medical sociology and gender studies, Barnes's research examines how medical authorities serve as cultural authorities on family building, fatherhood, motherhood, and childhood.

Personal life and education
Barnes was born in Fort Leavenworth, Kansas, and raised in Federal Way, Washington. She is the daughter of Larry Walther and Kathryn Walther (née Hiersche) and the oldest of five children. Barnes graduated from Federal Way High School in 1993 and earned a B.A. in media arts from Brigham Young University (1999). She completed MA and PhD degrees in Sociology from the University of California at San Diego (2005, 2011).

Career
Barnes is the author of Conceiving Masculinity: Male Infertility, Medicine, and Identity (Temple University Press 2014), based on ethnographic observations in infertility clinics, laboratories, and medical conferences and interviews with medical practitioners and patients. In 2015, Barnes was awarded the Book of the Year Prize by the Foundation for the Sociology of Health and Illness for "making the most significant contribution to the sub-discipline of medical sociology." Previous winners of the prize include Nelly Oudshoorn, Annemarie Mol, and Margaret Lock.

Barnes's research has been featured by several media websites, including TheAtlantic.com, NBCNews.com, ABCNews.com, Slate.com, TheGuardian.com, and TheTelegraph.com. She has been interviewed by Texas Public Radio, WHYY Philadelphia, and Voice of Russia UK.

In 2014 a TEDx talk given by Barnes was featured as an "Editor's Pick" on the TEDx homepage. The same year Barnes received a Future Research Leaders Award from the Economic and Social Research Council in the UK.

In 2016, Barnes received a grant from the National Science Foundation's Division of Social and Economic Sciences to write an ethnography of children's medicine.

Barnes has taught sociology courses at the University of Cambridge, Pacific University, Brigham Young University, University of California at San Diego, and Portland Community College.

References

American sociologists
American women sociologists
American ethnographers
Medical sociologists
Family sociologists
Year of birth missing (living people)
Living people
Brigham Young University alumni
University of California, San Diego alumni
Portland Community College faculty

Liberty Barnes


Claude de Beauharnais (22 September 1674 – 15 January 1738) was a French nobleman. He was sieur de Beaumont et de Bellechauve, captain des vaisseaux du roi, and a knight of the Order of Saint Louis. He was the son of François IV de Beauharnais, seigneur de La Boische and his wife Marie Marguerite-Françoise Puyvart de Chastullé.

A brother, François de Beauharnois was intendant of New France from 1702 to 1705. Another brother, Charles de Beauharnois served as Governor of New France from 1726 to 1746.

Claude de Beauharnois never resided in the colony but three times commanded the ships that restocked the troops in New France.

Marriage and issue
In 1713, Claude de Beauharnais married Renée Hardouineau (daughter of Pierre Hardouineau, seigneur de La Laudanière and his wife Renée Le Pays de Beauville). They had two children:
 François V de Beauharnais (8 February 1714 – 18 June 1800), seigneur de Beaumont et de Bellechauve, baron de Beauville, 1st marquis de la Ferté-Beauharnais.
 Claude de Beauharnais, 1st comte des Roches-Baritaud (1717–1784), who in 1753 married Marie-Anne-Françoise Mouchard (1738–1813) (three children, including Claude de Beauharnais).

Through his son François, Claude became grandfather of Alexandre de Beauharnais, and therefore the great-grandfather of Eugène de Beauharnais and Hortense de Beauharnais.

References

1680 births
1738 deaths
Claude de Beauharnais (1674-1738)
Knights of the Order of Saint Louis
People of New France

Claude de Beauharnais (1680–1738)


John Meeson Parsons (October 27, 1798 – March 26, 1870) was an art collector.

Parsons, youngest son of Thomas Parsons of Newport, Shropshire, was born at Newport, and educated by the Rev. Richard Thurstfield of Pattingham, then by the Rev. Francis Blick of Tamworth, and afterwards privately at Oxford; but hard reading brought on inflammation of the eyes, which obliged him to give up all study.

He then settled in the city of London, and became a member of the Stock Exchange. Early in his London career he took an interest in railways, was elected an associate of the Institution of Civil Engineers on 5 Feb. 1839, and on 9 Feb. 1843 became a director of the London and Brighton Railway Company, of which he was appointed chairman on 19 June 1843. In this office he was succeeded by Pascoe Grenfell on 11 April 1844, and ceased to be a director on 21 Aug. 1848. He was also a director of the Shropshire Union Railway from 1845 to 1849.

For many years he resided at 6 Raymond Buildings, Gray's Inn, and spent much of his time in collecting pictures and works of art. He had amassed at the time of his death a valuable gallery of pictures, principally of the German and Dutch schools, and of water-colour drawings by English artists. By his will he left to the trustees of the National Gallery, London, such of his oil paintings, not exceeding one hundred, as they might choose to select, and in case of their declining to accept the gift wholly or in part, then the same right of selection to the department of science and art at South Kensington. He also bequeathed to South Kensington any of his water-colours, sepia or charcoal drawings which they might be pleased to select, not exceeding one hundred. The trustees of the National Gallery selected only three, 'Fishing Boats in a Breeze off the West,' by J. M. W. Turner, and two paintings by P. J. Clays of Brussels. The department of science and art in June 1870 selected ninety-two oil and forty-seven water-colour paintings. A number of fine engravings were also left to the British Museum.

Parsons removed from 6 Raymond Buildings in November 1869 to 45 Russell Square, Bloomsbury, and died there aged 81. He married a daughter of John Mayhew, but was soon left a widower with one daughter, Ellen, who, on 16 May 1860, married Sir Charles William Atholl Oakeley, bart., of Frittenden House, Staplehurst, Kent.

References

Attribution

1798 births
1870 deaths
Newport, Shropshire
English art collectors
People from Newport, Shropshire

John Meeson Parsons


In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a die as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success (). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution.

An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes (r), the number of failures (n − r) are random because the total trials (n) are random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) before it breaks down.

The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use "negative binomial" or "Pascal" for the case of an integer-valued stopping-time parameter () and use "Polya" for the real-valued case.

For occurrences of associated discrete events, like tornado outbreaks, the Polya distributions can be used to give more accurate models than the Poisson distribution by allowing the mean and variance to be different, unlike the Poisson. The negative binomial distribution has a variance , with the distribution becoming identical to Poisson in the limit  for a given mean  (i.e. when the failures are increasingly rare).  This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term.

The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.

Definitions

Imagine a sequence of independent Bernoulli trials: each trial has two potential outcomes called "success" and "failure." In each trial the probability of success is  and of failure is . We observe this sequence until a predefined number  of successes occurs. Then the random number of observed failures, , follows the negative binomial (or Pascal) distribution:

Probability mass function

The probability mass function of the negative binomial distribution is

where r is the number of successes, k is the number of failures, and p is the probability of success on each trial.

Here, the quantity in parentheses is the binomial coefficient, and is equal to

There are k failures chosen from k + r − 1 trials rather than k + r because the last of the k + r trials is by definition a success.

This quantity can alternatively be written in the following manner, explaining the name "negative binomial":

Note that by the last expression and the binomial series, for every  and ,

hence the terms of the probability mass function indeed add up to one as below.

To understand the above definition of the probability mass function, note that the probability for every specific sequence of r successes and k failures is , because the outcomes of the k + r trials are supposed to happen independently. Since the rth success always comes last, it remains to choose the k trials with failures out of the remaining k + r − 1 trials. The above binomial coefficient, due to its combinatorial interpretation, gives precisely the number of all these sequences of length k + r − 1.

Cumulative distribution function

The cumulative distribution function can be expressed in terms of the regularized incomplete beta function:

(This formula is using the same parameterization as in the article's table, with r the number of successes, and  with  the mean.)

It can also be expressed in terms of the cumulative distribution function of the binomial distribution:

Alternative formulations
Some sources may define the negative binomial distribution slightly differently from the primary one here. The most common variations are where the random variable X is counting different things. These variations can be seen in the table here:

Each of the four definitions of the negative binomial distribution can be expressed in slightly different but equivalent ways. The first alternative formulation is simply an equivalent form of the binomial coefficient, that is: .  The second alternate formulation somewhat simplifies the expression by recognizing that the total number of trials is simply the number of successes and failures, that is: .  These second formulations may be more intuitive to understand, however they are perhaps less practical as they have more terms.
 The definition where X is the number of n trials that occur for a given number of r successes is similar to the primary definition, except that the number of trials is given instead of the number of failures.  This adds r to the value of the random variable, shifting its support and mean.
 The definitiond where X is the number of k successes (or n trials) that occur for a given number of r failures is similar to the primary definition used in this article, except that numbers of failures and successes are switched when considering what is being counted and what is given.  Note however, that p still refers to the probability of "success".
 The definition of the negative binomial distribution can be extended to the case where the parameter r can take on a positive real value.  Although it is impossible to visualize a non-integer number of "failures", we can still formally define the distribution through its probability mass function.  The problem of extending the definition to real-valued (positive) r boils down to extending the binomial coefficient to its real-valued counterpart, based on the gamma function:

 After substituting this expression in the original definition, we say that X has a negative binomial (or Pólya) distribution if it has a probability mass function:

 Here r is a real, positive number.

In negative binomial regression, the distribution is specified in terms of its mean, , which is then related to explanatory variables as in linear regression or other generalized linear models.  From the expression for the mean m, one can derive  and .  Then, substituting these expressions in the one for the probability mass function when r is real-valued, yields this parametrization of the probability mass function in terms of m:

The variance can then be written as .  Some authors prefer to set , and express the variance as .  In this context, and depending on the author, either the parameter r or its reciprocal α is referred to as the "dispersion parameter", "shape parameter" or "clustering coefficient", or the "heterogeneity" or "aggregation" parameter. The term "aggregation" is particularly used in ecology when describing counts of individual organisms. Decrease of the aggregation parameter r towards zero corresponds to increasing aggregation of the organisms; increase of r towards infinity corresponds to absence of aggregation, as can be described by Poisson regression.

Alternative parameterizations
Sometimes the distribution is parameterized in terms of its mean μ and variance σ2:

Examples

Length of hospital stay
Hospital length of stay is an example of real-world data that can be modelled well with a negative binomial distribution via negative binomial regression.

Selling candy
Pat Collis is required to sell candy bars to raise money for the 6th grade field trip.  Pat is (somewhat harshly) not supposed to return home until five candy bars have been sold.  So the child goes door to door, selling candy bars. At each house, there is a 0.6 probability of selling one candy bar and a 0.4 probability of selling nothing.

What's the probability of selling the last candy bar at the nth house?

Successfully selling candy enough times is what defines our stopping criterion (as opposed to failing to sell it), so k in this case represents the number of failures and r represents the number of successes.  Recall that the NegBin(r, p) distribution describes the probability of k failures and r successes in k + r Bernoulli(p) trials with success on the last trial.  Selling five candy bars means getting five successes.  The number of trials (i.e. houses) this takes is therefore k + 5 = n.  The random variable we are interested in is the number of houses, so we substitute k = n − 5 into a NegBin(5, 0.4) mass function and obtain the following mass function of the distribution of houses (for n ≥ 5):

What's the probability that Pat finishes on the tenth house?

What's the probability that Pat finishes on or before reaching the eighth house?

To finish on or before the eighth house, Pat must finish at the fifth, sixth, seventh, or eighth house. Sum those probabilities:

What's the probability that Pat exhausts all 30 houses that happen to stand in the neighborhood?

This can be expressed as the probability that Pat does not finish on the fifth through the thirtieth house:

Because of the rather high probability that Pat will sell to each house (60 percent), the probability of her NOT fulfilling her quest is vanishingly slim.

Properties

Expectation

The expected total number of trials needed to see r successes is . Thus, the expected number of failures would be this value, minus the successes:

Expectation of successes

The expected total number of failures in a negative binomial distribution with parameters  is r(1 − p)/p. To see this, imagine an experiment simulating the negative binomial is performed many times. That is, a set of trials is performed until  successes are obtained, then another set of trials, and then another etc. Write down the number of trials performed in each experiment:  and set . Now we would expect about  successes in total. Say the experiment was performed  times. Then there are  successes in total. So we would expect , so . See that  is just the average number of trials per experiment. That is what we mean by "expectation". The average number of failures per experiment is . This agrees with the mean given in the box on the right-hand side of this page.

A rigorous derivation can be done by representing the negative binomial distribution as the sum of waiting times. Let  with the convention  represents the number of failures observed before  successes with the probability of success being . And let  where  represents the number of failures before seeing a success. We can think of  as the waiting time (number of failures) between the th and th success. Thus

The mean is

which follows from the fact .

Variance
When counting the number of failures before the r-th success, the variance is r(1 − p)/p2.
When counting the number of successes before the r-th failure, as in alternative formulation (3) above, the variance is rp/(1 − p)2.

Relation to the binomial theorem

Suppose Y is a random variable with a binomial distribution with parameters n and p.  Assume p + q = 1, with p, q ≥ 0, then

Using Newton's binomial theorem, this can equally be written as:

in which the upper bound of summation is infinite.  In this case, the binomial coefficient

is defined when n is a real number, instead of just a positive integer.  But in our case of the binomial distribution it is zero when k > n.  We can then say, for example

Now suppose r > 0 and we use a negative exponent:

Then all of the terms are positive, and the term

is just the probability that the number of failures before the rth success is equal to k, provided r is an integer.  (If r is a negative non-integer, so that the exponent is a positive non-integer, then some of the terms in the sum above are negative, so we do not have a probability distribution on the set of all nonnegative integers.)

Now we also allow non-integer values of r.  Then we have a proper negative binomial distribution, which is a generalization of the Pascal distribution, which coincides with the Pascal distribution when r happens to be a positive integer.

Recall from above that

The sum of independent negative-binomially distributed random variables r1 and r2 with the same value for parameter p is negative-binomially distributed with the same p but with r-value r1 + r2.

This property persists when the definition is thus generalized, and affords a quick way to see that the negative binomial distribution is infinitely divisible.

Recurrence relations

The following recurrence relations hold:

For the probability mass function

For the moments

For the cumulants

Related distributions
 The geometric distribution (on { 0, 1, 2, 3, ... }) is a special case of the negative binomial distribution, with

 The negative binomial distribution is a special case of the discrete phase-type distribution.
 The negative binomial distribution is a special case of discrete compound Poisson distribution.

Poisson distribution
Consider a sequence of negative binomial random variables where the stopping parameter r goes to infinity, while the probability p of success in each trial goes to one, in such a way as to keep the mean of the distribution (i.e. the expected number of failures) constant. Denoting this mean as λ, the parameter p will be p = r/(r + λ)

Under this parametrization the probability mass function will be

Now if we consider the limit as r → ∞, the second factor will converge to one, and the third to the exponent function:

which is the mass function of a Poisson-distributed random variable with expected value λ.

In other words, the alternatively parameterized negative binomial distribution converges to the Poisson distribution and r controls the deviation from the Poisson.  This makes the negative binomial distribution suitable as a robust alternative to the Poisson, which approaches the Poisson for large r, but which has larger variance than the Poisson for small r.

Gamma–Poisson mixture
The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a  distribution, where λ is itself a random variable, distributed as a gamma distribution with shape r and scale   θ = or correspondingly rate β =.

To display the intuition behind this statement, consider two independent Poisson processes, "Success" and "Failure", with intensities p and 1 − p. Together, the Success and Failure processes are equivalent to a single Poisson process of intensity 1, where an occurrence of the process is a success if a corresponding independent coin toss comes up heads with probability p; otherwise, it is a failure. If r is a counting number, the coin tosses show that the count of successes before the rth failure follows a negative binomial distribution with parameters r and p. The count is also, however, the count of the Success Poisson process at the random time T of the rth occurrence in the Failure Poisson process. The Success count follows a Poisson distribution with mean pT, where T is the waiting time for r occurrences in a Poisson process of intensity 1 − p, i.e., T is gamma-distributed with shape parameter r and intensity 1 − p. Thus, the negative binomial distribution is equivalent to a Poisson distribution with mean pT, where the random variate T is gamma-distributed with shape parameter r and intensity . The preceding paragraph follows, because λ = pT is gamma-distributed with shape parameter r and intensity .

The following formal derivation (which does not depend on r being a counting number) confirms the intuition.

Because of this, the negative binomial distribution is also known as the gamma–Poisson (mixture) distribution. The negative binomial distribution was originally derived as a limiting case of the gamma-Poisson distribution.

Distribution of a sum of geometrically distributed random variables

If Yr is a random variable following the negative binomial distribution with parameters r and p, and support {0, 1, 2, ...}, then Yr is a sum of r independent variables following the geometric distribution (on {0, 1, 2, ...}) with parameter p. As a result of the central limit theorem, Yr (properly scaled and shifted) is therefore approximately normal for sufficiently large r.

Furthermore, if Bs+r is a random variable following the binomial distribution with parameters s + r and p, then

In this sense, the negative binomial distribution is the "inverse" of the binomial distribution.

The sum of independent negative-binomially distributed random variables r1 and r2 with the same value for parameter p is negative-binomially distributed with the same p but with r-value r1 + r2.

The negative binomial distribution is infinitely divisible, i.e., if Y has a negative binomial distribution, then for any positive integer n, there exist independent identically distributed random variables Y1, ..., Yn whose sum has the same distribution that Y has.

Representation as compound Poisson distribution
The negative binomial distribution NB(r,p) can be represented as a compound Poisson distribution: Let  denote a sequence of independent and identically distributed random variables, each one having the logarithmic series distribution Log(p), with probability mass function

Let N be a random variable, independent of the sequence, and suppose that N has a Poisson distribution with mean . Then the random sum

is NB(r,p)-distributed. To prove this, we calculate the probability generating function GX of X, which is the composition of the probability generating functions GN and GY1. Using

and

we obtain

which is the probability generating function of the NB(r,p) distribution.

The following table describes four distributions related to the number of successes in a sequence of draws:

(a,b,0) class of distributions

The negative binomial, along with the Poisson and binomial distributions, is a member of the (a,b,0) class of distributions. All three of these distributions are special cases of the Panjer distribution. They are also members of a natural exponential family.

Statistical inference

Parameter estimation

MVUE for p

Suppose p is unknown and an experiment is conducted where it is decided ahead of time that sampling will continue until r successes are found. A sufficient statistic for the experiment is k, the number of failures.

In estimating p, the minimum variance unbiased estimator is

Maximum likelihood estimation

When r is known, the maximum likelihood estimate of p is

but this is a biased estimate. Its inverse (r + k)/r, is an unbiased estimate of 1/p, however.

When r is unknown, the maximum likelihood estimator for p and r together only exists for samples for which the sample variance is larger than the sample mean. The likelihood function for N iid observations (k1, ..., kN) is

from which we calculate the log-likelihood function

To find the maximum we take the partial derivatives with respect to r and p and set them equal to zero:

 and

where

  is the digamma function.

Solving the first equation for p gives:

Substituting this in the second equation gives:

This equation cannot be solved for r in closed form. If a numerical solution is desired, an iterative technique such as Newton's method can be used. Alternatively, the expectation–maximization algorithm can be used.

Occurrence and applications

Waiting time in a Bernoulli process

For the special case where r is an integer, the negative binomial distribution is known as the Pascal distribution. It is the probability distribution of a certain number of failures and successes in a series of independent and identically distributed Bernoulli trials. For k + r Bernoulli trials with success probability p, the negative binomial gives the probability of k successes and r failures, with a failure on the last trial. In other words, the negative binomial distribution is the probability distribution of the number of successes before the rth failure in a Bernoulli process, with probability p of successes on each trial. A Bernoulli process is a discrete time process, and so the number of trials, failures, and successes are integers.

Consider the following example. Suppose we repeatedly throw a die, and consider a 1 to be a failure.  The probability of success on each trial is 5/6. The number of successes before the third failure belongs to the infinite set { 0, 1, 2, 3, ... }. That number of successes is a negative-binomially distributed random variable.

When r = 1 we get the probability distribution of number of successes before the first failure (i.e. the probability of the first failure occurring on the (k + 1)st trial), which is a geometric distribution:

Overdispersed Poisson

The negative binomial distribution, especially in its alternative parameterization described above, can be used as an alternative to the Poisson distribution.  It is especially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. In such cases, the observations are overdispersed with respect to a Poisson distribution, for which the mean is equal to the variance. Hence a Poisson distribution is not an appropriate model.  Since the negative binomial distribution has one more parameter than the Poisson, the second parameter can be used to adjust the variance independently of the mean. See Cumulants of some discrete probability distributions.

An application of this is to annual counts of tropical cyclones in the North Atlantic or to monthly to 6-monthly counts of wintertime extratropical cyclones over Europe, for which the variance is greater than the mean.  In the case of modest overdispersion, this may produce substantially similar results to an overdispersed Poisson distribution.

The negative binomial distribution is also commonly used to model data in the form of discrete sequence read counts from high-throughput RNA and DNA sequencing experiments.

Multiplicity Observations (Physics)

The negative binomial distribution has been the most effective statistical model for a broad range of multiplicity observations in particle collision experiments, e.g.,   (See  for an overview), and is argued to be a scale-invariant property of matter, providing the best fit for astronomical observations, where it predicts the number of galaxies in a region of space. The phenomenological justification for the effectiveness of the negative binomial distribution in these contexts remained unknown for fifty years, since their first observation in 1973. In 2023, a proof from first principles was eventually demonstrated by Scott V. Tezlaf, where it was shown that the negative binomial distribution emerges from symmetries in the dynamical equations of a canonical ensemble of particles in Minkowski space. Roughly, given an expected number of trials  and expected number of successes , where

an isomorphic set of equations can be identified with the parameters of a relativistic current density of a canonical ensemble of massive particles, via

where  is the rest density,  is the relativistic mean square density,  is the relativistic mean square current density, and , where  is the mean square speed of the particle ensemble and  is the speed of light—such that one can establish the following bijective map:

A rigorous alternative proof of the above correspondence has also been demonstrated through quantum mechanics via the Feynman path integral.

History

This distribution was first studied in 1713 by Pierre Remond de Montmort in his Essay d'analyse sur les jeux de hazard, as the distribution of the number of trials required in an experiment to obtain a given number of successes. It had previously been mentioned by Pascal.

See also
 Coupon collector's problem
 Beta negative binomial distribution
 Extended negative binomial distribution
 Negative multinomial distribution
 Binomial distribution
 Poisson distribution
 Compound Poisson distribution
 Exponential family
 Negative binomial regression
 Vector generalized linear model

References

Discrete distributions
Exponential family distributions
Compound probability distributions
Factorial and binomial topics
Infinitely divisible probability distributions

Negative binomial distribution


Roy Rogers (born Leonard Franklin Slye, November 5, 1911 – July 6, 1998) was an American singer and cowboy actor. Roy Rogers Restaurants chain was named after him. He and his third wife Dale Evans, his golden horse named Trigger, and his German Shepherd named Bullet were in more than 100 movies and The Roy Rogers Show. The show was on the radio and then on television from 1951 through 1957. His productions usually had a sidekick, usually either Pat Brady, (who drove a Jeep called "Nellybelle") or Andy Devine, or the crotchety George "Gabby" Hayes. Rogers' nickname was "King of the Cowboys."  Evans' nickname was "Queen of the West."

About Roy Rogers' life

Early life
Leonard Franklin Slye was born in Cincinnati, Ohio in USA. His parents' names were Andrew and Mattie Slye. His family lived in a tenement building on 2nd Street. (Riverfront Stadium was built at this place in 1970 and Leonard joked that he had been born at second base.) His father, Andrew Slye, was not happy with his job and city life. So, Andy Slye and his brother Will built a 12-by-50-foot houseboat from salvage lumber. In July 1912, the Slye family traveled up the Ohio River towards Portsmouth, Ohio, to pursue a more stable life in Portsmouth. They bought land on which they could build a home.
Because of the flood of 1913, they moved their houseboat to the land and thereafter continued living in the houseboat on dry land.

In 1919, the Slyes bought a farm in Duck Run, located near Lucasville, Ohio, 12 miles north of Portsmouth. There they built a six-room home. But the farm alone could not give a good income for his family, so Andrew took a job at a shoe factory in Portsmouth. He lived there during the week and returned home on weekends. He used to bring gifts for his family after paydays. One important gift was a horse which is how Leonard first learned how to ride.

Leonard attended high school in McDermott, Ohio. When he was 17, his family returned to Cincinnati. In Cincinnati, his father started work at another shoe factory. Leonard also wanted to help his family to earn more money, so he left high school. He started to work with his father at the shoe factory and went to night school.
Leonard was made fun of for sleeping in class, so he left night school.

Leonard and his father did not like their factory jobs. In 1929, his older sister, Mary, went to Lawndale, California, with her husband. Leonard and his father left their shoe factory jobs. The family lived with Mary for four months and then cam back to Ohio. Soon, Leonard got to go to California with Mary's husband's father. The rest of the family came to California in the spring of 1930.

The Slyes rented a small house close to Mary. Leonard and his father soon found jobs as truck drivers for a highway making project, but soon learned that their employer had become bankrupt. Then came the years of the Great Depression. The Slyes moved from job to job, collecting fruit and living in worker camps. One day, Andrew Slye learned about a shoe factory hiring in Los Angeles. Andrew asked Leonard to join him. Leonard felt happy playing guitar and singing around campfires and told his father that he wanted to earn money through music. His father agreed. Leonard and his cousin Stanley Slye went to Los Angeles and started performing as The Slye Brothers.

Leonard had by then come to be known as Len. In 1932, he met Lucile Ascolese while on tour. The same year, a palomino colt was born in Santa Cietro, CA. The young horse was first named "Golden Cloud," and later renamed "Trigger." In May 1933, Len, 21, proposed to Lucile, 19, on the radio. Len then went on tour with the "O-Bar-O Cowboys." In June 1933, Len met Grace Arlene Wilkins at a radio station in New Mexico. She gave Len a lemon pie in exchange for his singing "Swiss Yodel" on the radio. By August 1934, Len and Lucile had separated as she was jealous and tired of being a musician's wife. Len and Lucile divorced on June 8, 1936. Len and Grace Arlene Wilkins married in Roswell, New Mexico, on June 11, 1936.

In 1941, Len and his wife Grace adopted a girl, Cheryl Darlene. In 1942, they legally changed their names to Roy and Grace Arlene Rogers. The next year, Grace gave birth to a daughter, Linda Lou.

References

American television actors
Actors from Cincinnati
Singers from Ohio
1911 births
1998 deaths
Deaths from heart failure

Roy Rogers


Many sports playoffs and knockout tournaments include a third place playoff, third place match, bronze medal game, or consolation game to decide which competitor or team will be credited with finishing third and fourth. This game is typically competed by the competitors or teams that lost in the semi-finals of the tournament that they competed in. Some tournaments may use the third place playoff to determine who wins the bronze medal, while other tournaments need to hold a third place playoff for seeding purposes if three or all four semi-finalists advance to another tournament. Social psychology studies have found that bronze medalists who had won a third place playoff were significantly happier than silver medalists who had lost a championship final.

In tournaments that do not award medals or have the third place finisher advance to something else, a third place playoff is a classification match that serves little more than as a consolation to the losing semi-finalists. A consolation game also allows teams to play more than one game after having invested time, effort and money in the quest for a championship. Third place playoffs held as such consolation games are subject to debate. Many sports tournaments do not have a third place playoff due to a lack of interest. It has been criticised by some who feel that the match serves little purpose, but others see this game as an occasion for the losing semi-finalists to salvage some pride. How seriously the competitors or teams take a third place consolation game may also be mixed: a heavily favoured team that lost in an upset in the semi-final round may not have as much incentive to win as would a "Cinderella" team who was not expected to advance that far.

Olympics
Most sports using a knockout format in the Olympic Games have a third place playoff to determine who wins the bronze medal. As the difference between a bronze medal and no medal is quite significant, competitors still take this seriously.

The martial arts and combat sports events instead award two bronze medals. Since the 1952 Summer Olympics, boxing has automatically awarded bronze medals to both losing semi-finalists, on the grounds that there was not enough time to recover between the semi-final bouts and a third place bout. Judo, taekwondo, and wrestling also award two bronze medals, but these feature two bronze medal matches between the losing semi-finalists and the winners of the repechage.

Rugby World Cup
The Rugby World Cup used to give automatic qualification to all teams in the top three of the ongoing tournament to the one that would follow it four years later thus making the third place playoff game important, but this was later scrapped after the 1999 edition of the tournament allowing teams outside the top three to automatically qualify depending on their IRB co-efficient in the rankings.

FIFA World Cup and other association football tournaments
The 1980 edition was the last UEFA European Championship to have a third place match. That was the only third place match in the tournament's history to be decided by a penalty shootout, where Czechoslovakia defeated hosts Italy 9–8 on penalties after a 1-1 draw.

The FIFA World Cup features a third place playoff, usually on the day before the final. It is often there to provide a spectacle as there is often a gap of a few days between the semi-finals and the final. The third place playoff is considered a lower-priority match to organizers, as it is frequently scheduled in one of the smaller stadia; the largest stadium (usually located in the host nation's capital city) is reserved for the final, while the semi-finals occupy the second and third-largest stadia. However, the third place match in the 1994 World Cup did use the Rose Bowl stadium, the same venue that would later host the tournament final, setting a record attendance of 91,500 for a third place playoff in FIFA World Cup history.

The UEFA Nations League also has a third place playoff; this game is played prior to the final on the same day.

The third-place match in the FIFA Women's World Cup has been somewhat more important to the organizers – the 1999, 2003, and 2007 matches were all held in the same stadium as the final. In fact, the 1999 and 2007 third-place matches were both held as the first half of a doubleheader that culminated in the final. The 2011 third-place match returned to the more traditional scheduling of the day before the final in a different stadium. Notably, the 1999 third-place match was the curtain-raiser to the most-attended women's sporting event in history, the 1999 final also held in the Rose Bowl.

The third place match is generally a high-scoring affair, as no men's match has seen fewer than two goals scored since Poland's 1-0 win over Brazil in 1974, with four out of the last seven bronze-medal games, since 1994, seeing four goals or more. For tournament top scorers, the third place match's tendency of attacking football is a great opportunity to win the Golden Shoe, with players such as Salvatore Schillaci (1990), Davor Šuker (1998), and Thomas Müller (2010) getting the goal they needed to take sole possession of the lead. The FIFA Women's World Cup has had only eight editions to date, therefore creating less opportunity for a pattern to form. However, two of the third-place games in that competition have seen fewer than three goals. In 1995, the USA defeated China 2–0. In 1999, the third-place match between Brazil and Norway ended in a scoreless draw and penalty shootout (won by Brazil), as did the final between the USA and China (won by the USA). In 2015, the third place match between Germany and England was the first to go to extra time, and in the second period of extra time, England scored a single penalty and held on to the lead to upset Germany.

How seriously the competing teams take this match is subject to debate. Certain teams, especially ones which had been expected to reach the final, will rest some of their starters to allow some of their reserve team players to participate in a World Cup game. For instance French team captain Michel Platini did not play in either the 1982 or 1986 third place matches, while German goalkeeper Hans-Jörg Butt received his only competitive international appearance in a third place playoff, and Michel Vorm came on during injury time of the 3–0 third place play-off win against Brazil in Brasília thus ensuring that all 23 Dutch squad members played at the tournament. By contrast, teams that are not expected to get this far usually take this match seriously, as third place can be a historical achievement.  In the 1994 World Cup, the Sweden national team branded the game as "the bronze match" and after victory they landed at Arlanda with a fighter escort and were then paraded through the streets of Stockholm to millions live on national TV. Another example of a high-profile third place match was in 1998, when the recently established Croatian football team upset the Netherlands.

If the host nation is involved in the third place match, the team generally uses the match to thank the support of their fans (such as the South Korean football team in 2002, and the German football team in 2006). German goalkeeper Oliver Kahn, who had been a reserve to Jens Lehmann during the 2006 tournament, was allowed to retire in the third place playoff by then manager Jürgen Klinsmann. Germany and Portugal fielded strong lineups in that match, after both were narrowly eliminated in their respective semi-finals (Germany and Italy nearly went to penalties, while Portugal was defeated by France). For Brazil, the dismal 3–0 loss to the Netherlands in the 2014 third place match, along with the 7–1 semi-final defeat to Germany, led to coach Luiz Felipe Scolari being dismissed. For the Dutch, this was their first bronze medal in the FIFA World Cup.

Germany currently holds the most third-place finishes in the men's World Cup, with four, their most recent in 2010. Sweden has the most third-place finishes in the Women's World Cup, with four.

Professional basketball
The Big3 professional 3-on-3 basketball league features a post-season game for third place; the game is played directly before the league's championship and features the teams who were eliminated in the semifinals. The FIBA World Cup has a third-place game.

Little League World Series
For most of its history, the Little League World Series has featured either a consolation bracket, or consolation games. Currently, the tournament features a single consolation game between the United States runner-up and the International runner-up.  Like the championship, the game allows an American team to compete against an International team.  All other games are played within their respective American or International pool of eight teams each, except two exhibition games which match the United States teams and International teams which were doubly eliminated, and winless, in their respective brackets (these were eliminated following the 2019 LLWS).

Early season College Basketball Tournaments
Third place games (and consolation games for lower placings) are common in early season college basketball tournaments, as it gives each team an opportunity to play more games before the conference games start in earnest.  It also provides the tournament venue with additional games.

Defunct third-place playoff games
Many sports tournaments do not have a third place playoff, mostly due to a lack of interest from the competitors and also from the fans. Several of the most celebrated knockout tournaments – the FA Cup third-fourth place matches (1970–1974), the NCAA Men's Division I Basketball Championship (1946–1981) and the UEFA European Championships (1960-1980) – did feature the third place game for a period of time, but later abandoned it. The game was usually played immediately preceding the championship game, but was not nationally televised. For most of its years, the NCAA featured consolation games in both regional play and within the Final Four. However, as the field expanded beyond 32 teams, the game lost significance. Eliminating the game also allowed the losing teams to return home rather than remaining in the Final Four city for an additional two days to play a game holding less interest than the championship.

The National Football League had a consolation game, the Playoff Bowl, from  to , which pitted the second-place team in each of the two conferences (based on regular season record from 1960 to ) against each other in Miami, Florida. Through the 1966 season, the only scheduled NFL playoff game was the Championship Game (with unscheduled conference tie-breaker games as necessary; only once during the 1960s, in 1965, was this required.

In , the NFL playoff field expanded to four to include a division championship, with its first-round losers going to the Playoff Bowl, which had become increasingly unpopular with participating players, fans and officials. With interest declining for a third-place game, and an eight-team playoff field arriving with the AFL–NFL merger in , the Playoff Bowl was abandoned with minimal objection. One vestige of the Playoff Bowl survived into the 21st century: the losing coaches in each conference championship game coached the respective Pro Bowl squads from 1970-1978, and again from 1982-2008.

The Philippine Basketball Association, from its inception, also had third place games preceding its conferences' playoff finals until this was removed the end of the  season.

Criticism of use in the Page playoff system
Third place playoffs are especially controversial when they are used in tournaments that use a Page playoff system since there is only one semi-final game in this format.

Critics argue that in such a formula, the loser of the semi-final should simply be awarded third place, while proponents of the third place game argue that without it, the importance of the medal round is lowered since the top two teams heading into the Page playoff would otherwise be guaranteed a medal: this argument carries less weight in tournaments where medals are not awarded, or are considered of relatively minor importance in comparison to winning the tournament.

See also
 Classification match
 Knockout tournament
 Single-elimination tournament

References

Sports terminology

Third place playoff


George Anderson Cooke (July 3, 1869 – December 6, 1938) was a member of the Illinois General Assembly 1902-1909 and a judge of the Illinois Supreme Court 1909-1918, serving as chief justice 1913-1914.

Biography
Born in New Athens, Ohio, both of Cooke's parents died when he was 11 years old, and he was sent to live in Mercer County, Illinois. He was educated at Knox College, graduating in 1892.

Cooke was admitted to the bar of Illinois in 1895 and established a law practice in Aledo, Illinois.  In 1902, he was elected to the Illinois House of Representatives, representing the 33rd District. He served two terms.

Upon the death of Justice Guy C. Scott of the Illinois Supreme Court in 1909, Cooke ran for and won election to the Fourth District of the Illinois Supreme Court.  Cooke served out the remainder of Justice Scott's term and then won re-election to a full term in 1912.  He served as chief justice of the court for two consecutive terms in 1913 and 1914.

In 1918, Cooke left the bench to become chief counsel of the Peoples Gas Light and Coke Company, a position he held for the next twenty years until his death.

Cooke was married to Sarah Blee.  Together, they had four children.  He died in his home on December 6, 1938.

References
 "George A. Cooke, Ex-Chief Justice of Illinois, Dies." Chicago Daily Tribune, December 6, 1938; ProQuest Historical Newspapers Chicago Tribune (1849–1986). Pg. 9
 "George A. Cooke." Illinois Supreme Court Justice Archives. http://www.state.il.us/court/supremecourt/justicearchive/Bio_Cooke.asp

1869 births
1938 deaths
People from Aledo, Illinois
People from Harrison County, Ohio
Knox College (Illinois) alumni
Members of the Illinois House of Representatives
Chief Justices of the Illinois Supreme Court
Illinois lawyers
Justices of the Illinois Supreme Court

George A. Cooke