
vasaa-poonchh vitaran

vasaa-poonchh vitaran ack sambhavana vitaran haye joe ack samanya vitaran yaa ack ghaatiya vitaran key saapeksh ack badee tirchhaapan yaa curtosis pradarshit kartaa haye. aam upayog mein, vasaa-poonchh aur bhaari-poonchh vaale shabd kabhi-kabhi paryaayavaachi hotey hain; vasaa-poonchh vaale shabd koo kabhi-kabhi bhaari-poonchh vaale upasamuchchay key roop mein bhee paribhaashit kiya jaataa haye. vibhinn shodh samudaay kaafee hudd taka aitihaasik karanon seey ack yaa dusare kaa samarthan karate hain, aur donon kii sateek paribhasha mein antar hoe sakate hain.
vasaa-poonchh vitaran kaa anubhavjanya roop seey vibhinn kshetron mein saamana kiya gayaa haih bhautiki, prithvi vigyaan, arthshastra aur rajneeti vigyaan. vasaa-poonchh vitaran key varg mein way shamil hain jinaki poonchh shakti kaanoon kii tarah kshay hoe jaati haye, joe vaigyaanik saahitya mein unake upayog mein sandarbh kaa ack samanya bindu haye. halanki, vasaa-poonchh vitaran mein anya dheere-dheere kshay honey vaale vitaran bhee shamil hain, jaise kii logg-normal.
charam maamlaah ack shakti-kaanoon vitaran.
ack motee poonchh kaa sabse charam mamla ack vitaran dwara diyaa jaataa haye jisaki poonchh ack shakti kaanoon kii tarah kshay hoe jaati haye. 
arthaat, yadi yaadrichhik charr "x" key poorak sanchayi vitaran koo iss prakaar vyakt kiya jaa sakata haye
taba vitaran koo ack vasaa poonchh kahaa jaataa haye yadi sootra _ 2. aise moolyon key liye poonchh kaa vicharan aur tirchhaapan ganitiya roop seey avyakhyayit haye (shakti-niyam vitaran kaa ack vishesh guna), aur isaliye kissy bhee samanya yaa ghaatiya vitaran seey badaa haye. sootra _ 3 key moolyon key liye, ack motee poonchh kaa daavaa adhik aspasht haye, kyonki iss parameter seema mein, bhinnata, tirchhaapan aur curtosis seemit hoe sakate hain, joe sootra _ 4 key sateek moolya parr nirbhar kartaa haye, aur iss prakaar sambhaavit roop seey ack uchch-bhinnata samanya yaa ghaatiya poonchh seey chhota haye. yeh aspashtata aksar iss baare mein asahamati paida karati haye kii vasaa-poonchh vitaran kyaa haye yaa kyaa naheen haye. sootra _ 5 key liye, sootra _ 6 kshan anant haye, isaliye pratyek shakti niyam vitaran key liye, kuchh kshan anirdhaarit hain.
notah yahaan tilde sanketan "sootra _ 7" karyon key asymptotic samatulyata koo sandarbhit kartaa haye, jiska arth haye kii unakaa anupaat ack sthiraank kii or jaataa haye. dusare shabdon mein, lakshanheen roop seey, vitaran kii poonchh ack shakti niyam kii tarah kshay hoe jaati haye.
vasaa kii poonchh aur jokhim kaa anuman vikritiyaan.
vasaa-poonchh vitaran kii tulanaa mein, samanya vitaran mein, paanch yaa adhik maanak vichalan ("5-sigma ghatanaaen") dwara ausat seey vichalit honey vaali ghatnaaon kii sambhavana cumm hoti haye, jiska arth haye kii samanya vitaran mein atyadhik ghatnaaon kii sambhavana vasaa-poonchh vitaran kii tulanaa mein cumm hoti haye. vasaa-poonchh vitaran jaise kii kauchi vitaran (aur samanya vitaran koo chhodkar anya sabhi sthir vitaran) mein "anirdhaarit sigma" hotaa haye (adhik takniki roop seey, bhinnata anirdhaarit haye).
parinamswarup, jaba detta ack antarnihit vasaa-poonchh vitaran seey utpann hotaa haye, tou jokhim key "samanya vitaran" model mein jootaa-aur ack seemit namuna aakar parr sigma adharit (aavashyak roop seey) anuman lagaana-bhavishyasoochak kathinaaee (aur jokhim) kii sahee degree koo cumm karega. kaee-vishesh roop seey benoit mandelbrott key saath-saath nassim teleb-ney samanya vitaran model kii iss kamee koo nott kiya haye aur prastaav diyaa haye kii sthir vitaran jaise vasaa-poonchh vitaran aksar vitt mein paae jaane vaale parisampatti return koo niyantrit karate hain.
vikalp moolya nirdhaaran kaa black-schole model samanya vitaran parr adharit haye. yadi vitaran vaastav mein ack motee-poonchh vaalaa haye, tou model cumm keemat vaale vikalp hoga joe paise seey bahut baahar hain, kyonki 5 yaa 7-sigma ghatana kii sambhavana samanya vitaran kii bhavishyavani kii tulanaa mein bahut adhik haye.
arthshastra mein anuprayog.
vitt mein, vasaa kii poonchh aksar hoti haye lekin atirikt jokhim key kaaran unhein avaanchhaniya maanaa jaataa haye. udaaharan key liye, ack nivesh ranneeti mein ack varsh key baad apekshit laabh hoe sakata haye, joe kii isake maanak vichalan kaa paanch gunaa haye. ack samanya vitaran maanate hue, isaki viphalata (nakaratmak laabh) kii sambhavana duss laakh mein ack seey cumm haye; vyavhaar mein, yeh adhik hoe sakata haye. vitt mein ubharane vaale samanya vitaran aam taur parr aisaa isaliye karate hain kyonki kissy sampatti key moolya yaa moolya koo prabhaavit karane vaale kaarak ganitiya roop seey "achche vyavhaar" vaale hotey hain, aur kendriya seema pramey iss tarah key vitaran key liye pradaan kartaa haye. haalaanki, dardanaak "vaastavik duniya" kii ghatanaaen (jaise kii ack tail kaa jhataka, ack badaa corporate diwaliyapan, yaa ack raajneetik sthiti mein achaanak parivartan) aamtaur parr ganitiya roop seey achchi tarah seey vyavhaar naheen kii jaati hain.
aitihaasik udaharanon mein 1929 kii wall street crashes, black mandey (1987), dott-comm bubble, 2000 key dashak key anta mein vittiya sankat, 2010 kii aakasmik crashes, 2020 kaa share bajar crashes shamil hain.
aur kuchh mudraon kaa unpagging.
bajar pratiphal vitaran mein vasaa kii poonchh kii kuchh vyavhaar sambandhi utpatti bhee hoti haye (niveshak atyadhik ashawad yaa nirashawad joe bajar mein badee chaalon kaa kaaran banata haye) aur isaliye vyavhaar vitt mein adhyayan kiya jaataa haye.
vipanan mein, parichit 80-20 niyam aksar paaya jaataa haye (jaise.jee. "20 pratishat graahak rajaswa kaa 80 pratishat hissa hain") detta key antargat ack fait tail vitaran kii abhivyakti haye.
vasaa kii poonchh" vastu baajaron yaa record udyog mein bhee dekhi jaati haye, vishesh roop seey dhwani vigyaan key baajaron mein. saptahik record bikri parivartanon key laghuganak key liye sambhaavyata ghanatva kaary atyadhik leptocurtic haye aur ack sankeern aur badey adhikatam dwara visheshta haye, aur samanya vitaran mamle kii tulanaa mein ack motee poonchh dwara. doosari or, iss vitaran mein kewal ack motee poonchh haye joe chart mein pravesh karane vaale nae record key prachaar key kaaran bikri mein vriddhi seey judee haye.

