
samanya vitaran koo modein

+ \frac {1} {\sigma\sqrt {2\paai}}\, e ^ {-\frac {(x + \mu) ^ 2} {2\sigma ^ 2}} </math>
 . cdf = sootra _ 1
 . maadhya = sootra _ 2
 . madhyika = 
 . mode = 
 . bhinnata = sootra _ 3
 . tirchhaapan = 
 . curtosis = 
 . entropy = 
 . mgf = 
 . charr = 
 . machuara = 
mudaa huaa samanya vitaran samanya vitaran seey sambandhit ack sambhavana vitaran haye. samanya roop seey vitarit yaadrichhik charr "x" koo ausat "μ" aur bhinnata "σ" 2 key saath diyaa gayaa haye, yaadrichhik charr "y" = ."x". ack samanya vitaran haye. iss tarah key mamle kaa saamana taba kiya jaa sakata haye jaba kewal kuchh charr kaa parimaan darj kiya jaataa haye, lekin iska sanket naheen. vitaran koo "folded" kahaa jaataa haye kyonki "x" = 0 key baain or praayiktaa dravyamaan koo nirpeksh moolya laker fold kiya jaataa haye. ooshmaa chaalan key bhautiki mein, mudaa huaa samanya vitaran aadhe sthaan parr ooshmaa sameekaran kaa ack maulik samadhan haye; yeh mool key madhyam seey ack hyperplane parr ack poorna avaahak honey key anuroop haye.
paribhaashaaen.
ghanatva.
sambhaavyata ghanatva falan (pee. dee. aff.) dwara diyaa jaataa haye
x" ≤0 key liye, aur harr jagah 0. ack vaikalpik sutrikaran dwara diyaa jaataa haye
jahan kosh cosine hyperbolic falan haye. yeh nimnalikhit haye kii sanchayi vitaran kaary (see. dee. aff.) iss prakaar diyaa jaataa haih
x" ≤0 key liye, jahan erf () truti falan haye. yeh abhivyakti ardh-samanya vitaran key see. dee. aff. taka cumm hoe jaati haye jaba "aim. yuu" = 0 hotaa haye.
taba mudey hue vitaran kaa maadhya haye
yaa
jahan sootra _ 9 samanya sanchayi vitaran kaary haih
taba bhinnata koo maadhya key sandarbh mein aasaani seey vyakt kiya jaataa haih
mool samanya vitaran mein "x" key maadhya ("" ") aur vicharan (" "" 2) donon koo mudey hue vitaran mein "" y "key sthaan aur paimaane key maapdandon key roop mein vyakhya kii jaa sakati haye.
guna.
mode.
vitaran kaa tarika sootra _ 12 kaa moolya haye jisake liye ghanatva adhikatam kiya jaataa haye. iss moolya koo khojane key liye, humm sootra _ 12 key sambandh mein ghanatva kaa pahala vyutpann lete hain aur ise shoonya key barabar nirdhaarit karate hain. durbhagya seey, koee bund roop naheen haye. haalaanki, humm vyutpann koo behtar tareeke seey likh sakate hain aur ack gair-raikhik sameekaran key saath samaapt curr sakate hain.
sootra _ 14
sootra _ 15
sootra _ 16
sootra _ 17
sootra _ 18.
tsagris aur anya. (2014) sankhyaatmak jaanch seey dekhaa gayaa kii jaba sootra _ 19, adhikatam taba puuraa hotaa haye jaba sootra _ 20, aur jaba sootra _ 21 sootra _ 22 seey adhik hoe jaataa haye, tou adhikatam sootra _ 21 taka pahunchata haye. yeh nishchit roop seey kuchh apekshit haye, kyonki, iss mamle mein, samanya modd samanya vitaran mein parivartit hoe jaataa haye. nakaratmak bhinnataon key saath kissy bhee pareshani seey bachane key liye, parameter key ghatank kaa sujhaav diyaa jaataa haye. vaikalpik roop seey, aap ack baadha jodd sakate hain, jaise kii yadi anukulankarta ack nakaratmak bhinnata key liye jaataa haye tou logg-aajeevika kaa moolya naa yaa kuchh bahut chhota haye. 
visheshta kaary aur anya sambandhit kaary.
sootra _ 24.
sootra _ 25.
sootra _ 26.
sootra _ 27.
sootra _ 28.
saankhyikiya anuman.
maapdandon kaa anuman.
mudey hue samanya key maapdandon kaa anuman lagaane key kuchh tareeke hain. way sabhi anivarya roop seey adhikatam sambhavana anuman prakriya hain, lekin kuchh mamalon mein, ack sankhyaatmak adhikatamkaran kiya jaataa haye, jabaki anya mamalon mein, ack sameekaran key mool kii khoj kii jaa rahee haye. jaba aakar sootra 33 kaa namuna sootra upalabdh hotaa haye tou samanya modd kii logg-leaclehood koo nimnalikhit tareeke seey likhaa jaa sakata haye.
sootra _ 34
sootra _ 35
sootra _ 36
aar (prograaming bhasha) mein, package kaa upayog karke koee bhee vyakti vaastav mein teji seey millie praapt curr sakata haye (kamaand cock _ 1). vaikalpik roop seey, kamaand yaa iss vitaran mein fitt hoga. adhikatamkaran aasaan haye, kyonki dou mapdand (sootra _ 37 aur sootra _ 38) shamil hain. dhyaan dein kii sootra 37 key liye sakaratmak aur nakaratmak donon moolya sweekarya hain, kyonki sootra 37 sankhyaon kii vaastavik rekha seey sambandhit haye, isaliye, sanket mahatvapurna naheen haye kyonki vitaran isake sambandh mein samamit haye. agala code aar mein likhaa gayaa haye
folded <-function (y) {
 ##y sakaratmak detta vaalaa ack vector haye.
 n <-lambai (y) ##namuna aakar
 sy2 <-yog (y2)
 saim <-falan (paira, aine, aiss. aaee. 2) {
 mujhe <-paira [1]; seey <-exp (paira [2])
 f <-n/2 * logg (2/paaee/seey) + n * mujhe 2/2/seey +
 sy2/2/seey-yog (logg (kosh (mujhe * y/seey)))
 aff
 modd <-optim (see (mean (vaaee), sd (vaaee)), aine = aine, si2 = si2, saim, controll = list (maxit = 2000))
 modd <-optim (modd $paar, saim, aine = aine, aiss. aaee. 2 = aiss. aaee. 2, controll = list (maxit = 20000))
 parinam <-c (-modd $moolya, modd $paar [1], exp (modd $paar [2]))
 naam (parinam) <-c ("logg-aajeevika", "myu", "sigma varg")
 parinam
logg-aajeevika key aanshik vyutpann iss prakaar likhe jaate hain
sootra _ 41
sootra _ 42
sootra _ 43
sootra _ 44.
logg-aajeevika key pahale aanshik vyutpann koo shoonya seey jodkar, humm ack achchha sambandh praapt karate hain.
sootra _ 45.
dhyaan dein kii uparokt sameekaran key teen samadhan hain, ack shoonya parr aur dou vipareet sanket key saath. uparokt sameekaran koo logg-leakyhood doubleu key aanshik vyutpann mein pratisthaapit karke.aar.t sootra _ 46 aur ise shoonya key barabar karate hue, humm bhinnata key liye nimnalikhit abhivyakti praapt karate hain.
sootra _ 47,
joe samanya vitaran mein samaan sootra haye. yahaan ack mukhya antar yeh haye kii sootra 37 aur sootra 38 saankhyikiya roop seey swatantra naheen hain. uparokt sambandhon kaa upayog kushal punaraavarti tareeke seey adhikatam sambhavana anuman praapt karane key liye kiya jaa sakata haye. humm sootra _ 38 key liye ack praarambhik moolya seey shuru karate hain aur antim sameekaran key sakaratmak mool (sootra _ 37) koo paate hain. phir, hamein sootra _ 38 kaa ack adyatan moolya milata haye. prakriya taba taka dohrai jaa rahee haye jaba taka kii logg-lealyhood moolya mein parivartan naa key barabar naa hoe. ack aur aasaan aur adhik kushal tarika khoj algorithm kaa pradarshan karna haye. aaie humm antim sameekaran koo adhik suruchipurna tareeke seey likhein.
sootra _ 53
sootra _ 54.
yeh spasht hoe jaataa haye kii dou maapdandon key sambandh mein logg-aajeevika kaa anukoolan ack kaary kii mool khoj mein badal gayaa haye. yeh nishchit roop seey pichhali mool khoj key samaan haye. tsagris aur anya. (2014) ney dekhaa kii sootra _ 37, i key liye iss sameekaran key teen mool hain.ee. sootra 37 key teen sambhaavit maan hain joe iss sameekaran koo santusht karate hain. sootra _ 57 aur sootra _ 58, joe adhikatam sambhavana anuman hain aur 0, joe nyuntam logg-aajeevika seey mell khaata haye.

