
kohencha kappa

kohencha kappa gunank (κ, lahan akshar greek kappa) hii eka aakadevari aahe jee gunatmak (shrenibaddha) vastunsathi aantar-retter vishvasarhata (aanee intra-retter vishvasarhata) mojanyasathi vaparali jaate. sadharanpane haah eka adhik majboot upay manla jaato, joou sadhya takkevarichya kararachya gananepeksha adhik majboot aahe, kaaran 'κ' madhye yogayogane jhalela karar lakshat ghetala jaato. kararachya nirdeshankancha arth lavnyat yenanya adchanimule kohenchya kappabaddal vaad aahe. kahee sanshodhakanni asey suchavale aahe qee vastunmadhil matbhedache moolyankan karane sankalpanatmakdrushtya sope aahe.
itihas.
kappa sarkhya aakadevaricha pahila ullekh 1892 madhye galtonla deela gela.
kappala naveen tantra mhanoon sadar karnara moolbhut pepper jacob cohain yanni 1960 madhye 'shaikshanik aanee mansik mapan' yaa niyatkalikat prakashit keela hota.
vyakhya.
kohencha kappa done retarmadhil karar mojato jeey pratyek 'aine' vastunche 'see' paraspar vishisht shreninmadhye vargikaran karatat. sootra _ 1 chee vyakhya aahe
pratyek shreni yadruchchikpane pahana pratyek nirikshakachya sambhavyatechi ganana karnyasathi nirikshan kelelya detacha vapar karoon, mulyankankartyanmadhye sapeksh nirikshan kelela karar kuthe aahe aanee yogayog kararachi kalpanik sambhavyata aahe. jarr retter sampoorn sahmati darshavit asateel tarr sootra 3. jarr retarmadhye yogayogane apekshit asalelya goshtinvyatirikt konatahi karar nasel (dilelyapramane), tarr sootra 4. aakadevari nakaratmak asane shakya aahe, jee done retarchya retingmadhye konatahi sambandh naslyas yogayogane udbhavu shakate, kinwa bhinn raiting denyachi raterchi vastavik pravrutti pratibimbit karoo shakate.
shreninsathi, vargikaran karnyasathi nirikshane aanee sootra 5 andajit shrenichya kitee velah
heey khaleel bandhkamatun prapt jhaale aaheh
jethe sootra _ 8 hii andaje sambhavyata aahe qee retter 1 aanee retter 2 donhi samaan vastuche vargikaran k mhanoon kartil, tarr sootra _ 9 hii andaje sambhavyata aahe qee retter 1 ekhadya vastuche vargikaran k mhanoon karel (aanee tyachpramane retter 2 sathee).
sambandh sootra _ 10 heey done raterche moolyankan swatantra aahe yaa gruhitakacha vapar karnyavar aadharit aahe. sootra _ 9 yaa shabdacha andaj, k bhagile retter 1 (sootra _ 12) bhagile ekoon itum vaparoon, (sootra _ 13): sootra _ 14 (aanee tyachpramane retter 2 sathee) mhanoon vargikrut kelelya vastunchi sankhya vaparoon lavala jaato.
dwaiti vargikaran gondhal matricks.
dwaiti vargikarananche moolyankan karnyasathi yantra shikshan aanee sankhyikimadhye vaparlya jaanarya paramparik 2x2 gondhal matrixmadhye, kohenche kappa sootra asey lihile jaau shakateh
jethe tii. pii. heey kharey sakaratmak aahet, eff. pii. heey khote sakaratmak aahet, tii. aine. heey kharey nakaratmak aahet aanee eff. aine. heey khote nakaratmak aahet. yaa prakaranat, kohencha kappa haah havamanshastrat dnyat asalelya "hedke kaushalya guna" chya samatulya aahe. 1888 madhye myric haskell doolitalne haah upay pahilyanda sadar keela.
udaharane.
sadhe udaharan.
samaja tumhi anudanasathi arj karananya 50 lokanchya gatashi sambandhit mahitiche vishleshan karat hota. pratyek anudan prastav done vachakanni vachala aanee pratyek vachkane prastavala ektar 'hoy' kinwa 'nahee' mhatale. samaja matbhed mojanichi mahitee khalilpramane hotee, jethe aaa aanee buub vachak aahet, matrixchya mukhya karnavaril mahitee (aaa aanee dii) kararanchi sankhya mojate aanee karnabahya mahitee (buub aanee see) matbhedanchi sankhya mojate.
eae.jee.
nirikshan kelela pramanbaddh karar assa aaheh
ganana karnyasathi (yadruchchik kararachi sambhavyata) aapan nondavato keeh
tyamule donhi yadruchchikpane hoow mhanatil ashee apekshit sambhavyata ashee aaheh
tyachpramaneh
ekoon yadruchchik karar sambhavyata mhanje teey ektar hoy kinwa nahee yavar sahmat asalyachi sambhavyata, i.eae.:
tarr aata kohenchya kappasathi aapale sootra lagoo kelyane aaplyala milateh
samaan takkewari parantu bhinn sankhya.
done jodyanchya retarsathi mojalya gelelya kappachi tulana pratyek joditil done ratershee samaan takkewari karar asalelya done ratershee kartana kohenchya kappamadhye kadhikadhi samasya manali jaanari cases udbhavate parantu eka jodee pratyek vargat samaan sankhyene raiting dete tarr dusari jodee pratyek vargat khoop bhinn sankhyene raiting dete. (khaleel prakarananmadhye, pahilya prakaranat, soochana buub madhye 70 hoow aanee 30 sankhya aahet, parantu tyaa sankhya dusya prakaranat ulatya aahet.) udaharanarth, pudhil done prakarananmadhye pratyek vargatil kararachya babatit aaa aanee buub (donhi prakarananmadhye 100 paiki 60) yanchyat samaan karar aahe, mhanoon kohenchya kappachya sapeksh moolyanni heey pratibimbit karanyachi aamhi apeksha karoo. tathapi, pratyekasathi kohenchya kappyachi ganana karaneh
aaplyala aadhalate qee pahilya prakaranachya tulanet dusya prakaranat teey aaa aanee buub yanchyat adhik samanata darshavate. yache kaaran asey qee takkewari karar samaan asala taree, 'yogayogane' honara takkewari karar pahilya prakaranat lakshaniyaritya jaast aahe (0.40 chya tulanet 0.05).
malmatta.
gruhitak chachani aanee aatmavishvas antaral.
kappasathi pii-moolya kvachitach nondavale jaate, bahudha kaaran kappachi tulanene qamee moolye dekhil shoonyapeksha lakshaniyaritya vegali asoo shakatat parantu tapaskartyanna santusht karnyasathi pureshi pariman nasatat.
tarihi, tyachya pramanit trutiche varnan kele gele aahe
aanee vividh sanganak programdware ganana kelee jaate.
jarr aapan khaleel sootra vaparoon, amaryad sankhyetil vastoo tapasalya asateel tarr, apekshit kappa mulyansathi kappa sathee vishvasache antar tayar kele jaau shakateh
jethe sootra _ 24 heey manak samanya takkewari asate jevha sootra _ 25, aanee sootra _ 26
heey aakadevaritun andajit kelelya goshtinkade durlaksh karoon aanee asymptotic normalitycha vapar kartana bionomial vitaranachi andajit sambhavyata mhanoon vicharat gheuun mojale jaate (i.eae.: asey gruheet dharoon qee vastunchi sankhya mothee aahe aanee tee 0 kinwa 1 chya jawal nahee). bootstrap paddhati vaparoon sootra _ 27 (aanee sarvasadharanpane see. aay.) chaa andaj dekhil lavala jaau shakato.
parimanacha arth lavane.
jarr sankhyikeey mahatva heey upayukt margdarshak nasel, tarr kappache pariman purese karar darshavate? margdarshak tattve upayukt thartil, parantu kararavyatirikt itar ghatak tyachya parimanavar prabhav takoo shakatat, jyamule dilelya parimanacha arth lavane samasyapradhan banate. siim aanee rait yanni namood kelyapramane, done mahattvache ghatak mhanje prasar (code samatulya aahet kinwa tyanchya sambhavyatet farak aahe qaa) aanee purvagrah (done nirikshakansathi samaan kinwa bhinn kirkol sambhavyata aahet). itar goshti samaan asalyane, jevha code samatulya asatat tevha kappa jaast asatat. dusarikade, jevha done nirikshakandware code asampramanat vitarit kele jaatat tevha kappa jaast asatat. sambhavyatetil badalanchya ulat, jevha kappa lahan asato tevha purvgrahacha parinam motha asato tyapeksha jaast asato.
aanakhi eka ghatak mhanje kodchi sankhya. kodchi sankhya jasjashi vadhate tasatase kappa jaast hotat. anukaran abhyasavar aadharit, beckman aanee tyanchya sahakanyanni assa nishkarsh kadhala qee, trutipurna nirikshakansathi, code qamee asatana kappasathichi moolye qamee hotee. aanee, vyapkanvishayi siim andd riteschya vidhanashi sahmat, jevha code sadharanpane samatulya hote tevha kappa jaast hote. tyamule beckman aanee itar. kappache konatehi eka moolya sarvatrikpane swikararh manale jaau shakat nahee" assa nishkarsh kadhala."teey eka sanganak karyakram dekhil pradan karatat joou vaparkartyanna kodchi sankhya, tyanchi sambhavyata aanee nirikshakanchi achookata nirdisht karoon kappasathi mulyanchi ganana karoo deto. udaharanarth, 85 takke achook asalele samatulya sanket aanee nirikshak dilele asalyas, jevha kodchi sankhya anukrame 2,3,5 aanee 10 asate tevha kappache moolya 0.09,0.60,0.66 aanee 0.69 asate.
tathapi, sahityamadhye pariman margdarshak tattve disun aalee aahet. kadachit pahila hota landies aanee koch,
jyane <0 mulyanche varnan konatehi karar naan darshavinare aanee 0-0.20 kirkol, 0.21-0.40 nyayya, 0.41-0.60 madhyam, 0.61-0.80 lakshaniy aanee 0.81-1 jawaljawal paripoorn karar mhanoon kele. matra, margdarshak tattvancha haah sanch konatyahi prakare sarvatrikpane swikarla jaat nahee; landies aanee koch yanni vaiyaktik matavar aadharit, tyache samarthan karnyasathi konatahi purava puravala nahee. hii margdarshak tattve upayukt asanyapeksha adhik hanikarak asoo shakatat heey lakshat aale aahe. fleeschya samaan aniyantrit margdarshak tattvanmadhye 0.75 peksha jaast asalelya kappanna utkrusht, 0.40 teey 0.75 changalyachya babatit yogya aanee 0.40 peksha qamee asalelya kappanna kharab asey mhatale aahe.
kappa kamal.
jevha donhi nirikshak samaan code vitarit karatat, mhanje jevha sambandhit pankti aanee stambhanchi berries samaan asate tevhach kappa tyache saiddhantik kamal moolya 1 gruheet dharato. kahihi qamee mhanje paripoorn kararapeksha qamee asate. tarihi, asman vitaran dile tarr kappa sadhya karoo shakanare kamal moolya pratyakshat prapt jhalelya kappachya mulyacha arth lavnyas madat karate. κ" kamalche samikaran asey aaheh
jethe sootra _ 29, nehmipramane, sootra _ 30,
"k" = sanketanchi sankhya, sootra _ 31 heey pankti sambhavyata aahet aanee sootra _ 32 heey stambh sambhavyata aahet.
maryada.
kappa haah eka nirdeshank aahe joou baseline kararachya sandarbhat nirikshan kelelya kararacha vichar karato. tathapi, tapaskartyanni kappacha aadharbhut karar vishisht sanshodhan prashnasathi sambandhit aahe qee nahee yacha kaljipurvak vichar keela pahije. kappachya aadharresheche varanvar yogayogamule jhalela karar asey varnan kele jaate, jeey keval anshatah barobar aahe. kappacha aadharbhut karar haah assa karar aahe joou yadruchchik vatpachyamule apekshit asel, varg aakasmikta taktachya kirkol ekunanni nirdisht kelelya pramanat. asha prakare, jevha nirikshan kelele vatap varvar pahata yadruchchik asate, tevha marginal totaldware maryadit asalelya pramanat matbhed asale taree, κ = 0. tathapi, anek arjansathi, tapaskartyanna varg aakasmikta taktachya karnavaril atirikt mahitidvare varnan kelyapramane vatap asahmatipeksha kirkol ekunatil praman asahmatimadhye adhik swarasya asale pahije. asha prakare anek upayogansathi, kappachi aadharrekha dnyanvardhak asanyapeksha adhik vichalit karnari aahe. khaleel udaharan vicharat ghyah
asahmatiche praman 14/16 kinwa 0.875 aahe. matbhed pramanamule aahe kaaran vatap ishtatam aahe. κ heey 0.01 aahe.
asahmatiche praman 2/16 kinwa 0.125 aahe. matbhed heey vatpachyamule aahe kaaran praman samaan aahe. kappa − 0.07 aahe.
yethe, praman aanee vatpababat matbhed nondavane mahitipurn aahe tarr kappa mahitee aspasht karato. shivay, kappa heey gunottar asalyamule, kappa heey ganana aanee arth lavnyamadhye kahee aavhane aanate. vibhajkamadhil shoonyamule kappache gunottar anirdharit moolya parat karane shakya aahe. shivay, gunottar tyacha ansh kinwa tyacha chhed ughad karat nahee. sanshodhakanni praman aanee vatap yaa done ghatakanmadhye matbhed nondavane adhik mahitipurn aahe. heey done ghatak ekach saransh aakadevaripeksha shreninmadhil sambandh adhik spashtapane varnan karatat. jevha andajatmak achookata heey uddisht asate, tevha sanshodhak kappachya eka gunottarapeksha praman aanee vatpachya done ghatakancha vapar karoon andaj sudharnyachya margambaddal adhik sahajpane vichar karoo shakatat.kahee sanshodhakanni nirikshan kelelya shreninchi varanvarta dilelyapramane ghenyachya κ chya pravruttibaddal chinta vyakt kelee aahe, jyamule durmil roganchya nidanasarkhya paristhitit karar mojane avishvasaniy houu shakate. asha paristhitit, κ durmil shrenivaril kararala qamee lekhanyacha cull asato. yaa karanastav, κ haah kararacha atee rudhivadi upay manla jaato. itar lock yaa davyala virodh karatat qee kappa haah sandhicha karar "vicharat gheto". heey prabhavipane karnyasathi, sandhicha purvaniyojit nirnayanvar kassa parinam hoto yache spasht pratirup aavashyak aahe. kappa aakadevariche tathakathit sandhee samayojan asey manate qee, jevha purnapane nishchit nasate, tevha retter fakt andaj lavtat-eka atishay avastav paristhiti. shivay, kahee kamanni heey dakhavun dile aahe qee kappa aakadevari asantulit mahitisathi chukichya nishkarshaparyant kase neuu shakate. 
sambandhit aakadevari.
scots paee.
paee navachi ashich aakadevari scotney (1955) prastavit kelee hotee. kohencha kappa aanee scotcha paee heey kase mojale jaate yachya drushtine bhinn aahet.
flees 'kappa.
lakshat ghya qee kohencha kappa keval done retarmadhil karar mojato. donpeksha jaast retter asatana vaparlya jaanarya kararachya samaan mojamapasathi (flees 'kappa), flees (1971) pahaa. flees kappa heey matra, scotchya paee aakadevariche bahu-retter samanyikaran aahe, kohenchya kappache nahee. machine learningmadhil kamgirichi tulana karnyasathi dekhil kappacha vapar keela jaato, parantu mahitipurnata kinwa yoodenchi jeey sankhyiki mhanoon olakhali jaanari dishatmak aavrutti paryavekshit shikshanasathi adhik yogya asalyacha yuktivad keela jaato.
bharit kappa.
bharit kappa matbhedanna vegalya prakare bharit karnyas anumati dete aanee code aurder kelyavar visheshtah upayukt tharate. teen matricks samavisht aahet, nirikshan kelelya gunanche matricks, sandhee kararavar aadharit apekshit gunanche matricks aanee vajan matricks. karnavar (varchya-davya teey khalchya-ujavya) asalelya vajan matricks peshi karar darshavtat aanee asha prakare tyat shoonya asatat. karnabahya peshinmadhye tyaa asahmatiche gambhirya darshavinare vajan asate. byavachada, karnabaheril eka peshiche vajan 1 asate, tyaa donche vajan 2 asate, ityadi.
bharit κ chey samikaran asey aaheh
jethe "k" = sanketanchi sankhya aanee sootra _ 34, sootra _ 35 aanee sootra _ 36 heey anukrame vajan, nirikshan aanee apekshit matrixmadhil ghatak aahet. jevha karn peshinmadhye 0 chey vajan aanee serve karnabahya peshinche vajan 1 asate, tevha heey sootra varr dilelya gananepramanech kappache samaan moolya nirman karate.