Gaussian vs Normal Distribution
Ua ntej thiab qhov tseem ceeb tshaj qhov kev faib tawm ib txwm thiab Gaussian kev faib tawm yog siv los xa cov kev faib tawm tib yam, uas yog kab tias feem ntau ntsib kev faib tawm hauv kev txheeb cais.
Rau qhov sib txawv ntawm qhov sib txawv x nrog Gaussian lossis Kev faib tawm ib txwm, qhov muaj feem cuam tshuam kev faib tawm yog P(x)=[1/(σ√2π)] e^(-(x-µ) 2 /2σ2); qhov twg µ yog qhov nruab nrab thiab σ yog tus qauv sib txawv. Lub luag haujlwm ntawm lub luag haujlwm yog (-∞, +∞). Thaum npaj, nws muab lub tswb nrov nrov, raws li feem ntau raug xa mus rau hauv social sciences, lossis Gaussian nkhaus hauv kev tshawb fawb lub cev. Cov kev faib tawm ib txwm yog ib qho subclass ntawm elliptical distributions. Nws tseem tuaj yeem suav tias yog qhov txwv ntawm qhov kev faib tawm binomial, qhov twg tus qauv loj yog infinite.
Kev faib tawm ib txwm muaj cov yam ntxwv tshwj xeeb. Rau ib qho kev faib tawm, qhov nruab nrab, hom, thiab qhov nruab nrab yog tib yam, uas yog µ. Lub skewness thiab kurtosis yog xoom, thiab nws tsuas yog ib qho kev faib tawm tas mus li nrog tag nrho cov cumulants tshaj thawj ob (qhov nruab nrab thiab qhov sib txawv) yog xoom. Nws muab qhov muaj peev xwm ceev ua haujlwm nrog qhov siab tshaj plaws entropy rau txhua qhov txiaj ntsig ntawm qhov tsis muaj µ thiab σ2. Qhov kev faib tawm ib txwm yog nyob ntawm qhov kev txwv hauv nruab nrab, thiab nws tuaj yeem txheeb xyuas tau siv cov txiaj ntsig ua tau raws li qhov kev xav.
Qhov kev faib ib txwm tuaj yeem ua qauv siv kev hloov pauv z=(X-µ) / σ, uas hloov nws mus rau kev faib nrog µ=0 thiab σ=σ 2=1. Qhov kev hloov pauv no tso cai rau cov khoom siv tus nqi thiab ua kom yooj yim los daws cov teeb meem ntsig txog qhov muaj nuj nqi ntau yam thiab cov kev faib khoom xa mus.
Daim ntawv thov kev faib tawm ib txwm tuaj yeem faib ua peb chav kawm. Kev faib khoom ib txwm muaj, kwv yees li ib txwm faib, thiab ua qauv lossis xav tias kev faib khoom ib txwm muaj. Cov kev faib tawm ib txwm tshwm sim hauv qhov xwm txheej. Qhov ceev ntawm qhov kub thiab txias los yog zoo tagnrho roj molecules thiab hauv av lub xeev ntawm quantum harmonic oscillators qhia ib txwm faib. Kwv yees li ib txwm kev faib tawm tshwm sim hauv ntau qhov xwm txheej piav qhia los ntawm lub hauv paus txwv txoj kev xav. Binomial probability faib thiab Poisson faib, uas yog discrete thiab tas mus li feem, qhia ib tug zoo li ib txwm tis ntawm cov qauv siab heev.
Hauv kev xyaum, feem ntau ntawm cov kev sim ntsuas, peb xav tias qhov kev faib tawm yog qhov qub, thiab cov qauv kev xav uas ua raws li qhov kev xav ntawd. Raws li qhov tshwm sim, qhov tsis tuaj yeem xam tau yooj yim rau cov pej xeem thiab cov txheej txheem inference yuav yooj yim dua.
Dab tsi yog qhov txawv ntawm Gaussian Distribution thiab Ib txwm faib?
• Gaussian kev faib tawm thiab kev faib tawm ib txwm yog ib qho thiab tib yam.
