Poisson Distribution vs Normal Distribution
Poisson thiab Ib txwm faib tawm los ntawm ob txoj hauv kev sib txawv. Poisson yog ib qho piv txwv rau Discrete Probability Distribution whereas Normal belongs to Continuous Probability Distribution.
Kev faib tawm ib txwm yog feem ntau hu ua 'Gaussian Distribution' thiab siv tau zoo tshaj plaws los ua qauv teeb meem uas tshwm sim hauv Natural Sciences thiab Social Sciences. Muaj ntau yam teeb meem nyuaj tau ntsib siv qhov kev faib tawm no. Feem ntau cov piv txwv yuav yog 'Kev Saib Xyuas Tsis Zoo' hauv ib qho kev sim tshwj xeeb. Kev faib tawm ib txwm ua raws li cov duab tshwj xeeb hu ua 'Tswb nkhaus' uas ua rau lub neej yooj yim dua rau kev ua qauv ntawm ntau qhov sib txawv. Nyob rau lub sijhawm no ib txwm muaj kev faib tawm los ntawm 'Central Limit Theorem' nyob rau hauv uas tus lej loj ntawm qhov txawv txav tau faib 'ib txwm'. Qhov kev faib tawm no muaj symmetric faib txog nws txhais tau tias. Uas txhais tau tias sib npaug ntawm nws qhov x- tus nqi ntawm 'Peak Graph Value'.
pdf: 1/√(2πσ^2) e^(〖(x-µ)〗^2/(2σ^2))
Cov kab zauv hais saum toj no yog Qhov Muaj Peev Xwm Ceev Ua Haujlwm ntawm 'ib txwm' thiab los ntawm qhov loj, µ thiab σ2 hais txog 'txhais tau' thiab 'variance' feem. Qhov feem ntau ntawm cov kev faib tawm ib txwm yog 'Txheej Txheem Kev faib tawm' qhov twg µ=0 thiab σ2=1. Qhov no txhais tau hais tias pdf ntawm cov khoom tsis yog tus qauv ib txwm faib piav qhia tias, tus nqi x-tus nqi, qhov twg lub ncov tau raug hloov mus thiab qhov dav ntawm lub tswb tau raug muab faib los ntawm qhov tseem ceeb σ, uas tom qab hloov kho raws li 'Standard Deviation' lossis square root ntawm 'Variance' (σ^2).
Ntawm qhov tod tes, Poisson yog ib qho piv txwv zoo meej rau cov xwm txheej tsis sib xws. Qhov ntawd los raws li qhov txwv ntawm qhov kev faib tawm binomial - qhov sib faib ntawm 'Discrete Probability Variables'. Poisson yuav tsum tau siv thaum muaj teeb meem nrog cov ntsiab lus ntawm 'tus nqi'. Qhov tseem ceeb tshaj, qhov kev faib tawm no yog qhov txuas ntxiv yam tsis muaj kev so rau ib ntus ntawm lub sijhawm nrog qhov kev paub tshwm sim. Rau 'kev ywj pheej' cov xwm txheej ib qho txiaj ntsig tsis cuam tshuam qhov tshwm sim tom ntej yuav yog lub sijhawm zoo tshaj plaws, qhov twg Poisson los ua si.
Yog li tag nrho ib qho yuav tsum saib tias ob qho kev faib tawm yog los ntawm ob qhov kev xav sib txawv, uas ua txhaum qhov feem ntau sib xws ntawm lawv.
