Nkag Siab Txog Skewness thiab Kurtosis
Kev suav lej yog ib ceg tseem ceeb ntawm kev tshawb fawb hauv ntau qhov kev tshawb fawb, txij li kev tshawb fawb txog zej zog mus rau kev tshawb fawb txog ntuj. Hauv kev tshuaj xyuas cov ntaub ntawv, kev nkag siab txog kev faib tawm cov ntaub ntawv yog qhov tseem ceeb rau kev kos cov lus xaus kom raug thiab ntseeg tau. Ob lub ntsiab lus tseem ceeb uas siv ntau zaus hauv kev piav qhia txog kev faib tawm yog skewness thiab kurtosis. Tsab xov xwm no yuav tham txog cov lus txhais, kev txhais lus, thiab qhov tseem ceeb ntawm skewness thiab kurtosis hauv kev tshuaj xyuas cov ntaub ntawv.
Kev tsis sib haum xeeb
Kev Txhais ntawm Skewness
Skewness yog ib qho kev ntsuas ntawm qhov tsis sib xws ntawm qhov kev faib tawm ntawm qhov muaj feem ntawm ib qho random variable. Hauv cov lus yooj yim dua, skewness piav qhia txog qhov deb npaum li cas qhov kev faib tawm ntawm cov ntaub ntawv tawm ntawm ib qho zoo meej symmetrical, hu ua kev faib tawm ib txwm lossis Gaussian distribution.
Hom Kev Tsis Sib Haum
1. Qhov Sib Npaug Zoo: Kev faib cov ntaub ntawv uas ntev mus rau sab xis. Tus nqi sib npaug zoo qhia tias feem ntau ntawm cov ntaub ntawv tau sib sau ua ke rau sab laug, nrog rau tus tw sab xis ntev dua. Piv txwv li, cov nyiaj tau los ntawm ib tus neeg hauv ib pawg neeg feem ntau qhia txog qhov sib npaug zoo.
2. Kev Tsis Sib Npaug: Kev faib cov ntaub ntawv uas sib npaug rau sab laug. Hauv qhov no, tus nqi tsis sib npaug qhia tias feem ntau ntawm cov ntaub ntawv nyob rau sab xis, nrog rau sab laug ntev dua. Ib qho piv txwv feem ntau yog cov qhab nia xeem uas feem ntau ntawm cov tub ntxhais kawm tau qhab nia siab.
3. Kev Faib Tawm Symmetrical: Yog tias tus nqi skewness ze rau xoom, qhov kev faib tawm cov ntaub ntawv tuaj yeem suav tias ze rau symmetrical, xws li kev faib tawm ib txwm muaj.
Yuav Ua Li Cas Xam Skewness
Skewness tuaj yeem suav nrog siv cov qauv hauv qab no:
\[ \text{Skewness} = \frac{n}{(n-1)(n-2)} \sum \left(\frac{x_i – \bar{x}}{s}\right)^3 \]
Qhov twg:
– \( n \) = tus naj npawb ntawm cov ntaub ntawv,
– \( x_i \) = tus nqi ntawm tus kheej,
– \( \bar{x} \) = qhov nruab nrab ntawm cov ntaub ntawv,
-\( s\) = qhov sib txawv ntawm tus qauv.
Kev Txhais Lus ntawm Skewness
Kev txhais lus ntawm cov nqi skewness tuaj yeem pab nkag siab txog cov yam ntxwv ntawm cov ntaub ntawv faib tawm. Ua ib qho kev qhia dav dav:
- Skewness los txog 0 qhia txog kev faib tawm symmetric.
- Qhov skewness zoo qhia txog kev faib tawm uas skewed mus rau sab xis.
- Qhov tsis zoo skewness qhia txog kev faib tawm uas skewed mus rau sab laug.
Qhov Tseem Ceeb ntawm Skewness hauv Kev Tshawb Fawb Cov Ntaub Ntawv
Skewness yog ib qho cuab yeej tseem ceeb hauv kev tshuaj xyuas cov ntaub ntawv vim nws muab cov ntaub ntawv hais txog kev faib tawm ntawm cov ntaub ntawv uas tsis tuaj yeem pom los ntawm kev saib qhov nruab nrab lossis tus qauv sib txawv. Kev nkag siab zoo txog skewness tuaj yeem pab txiav txim siab seb qhov kev hloov pauv ntaub ntawv twg yog qhov tsim nyog rau kev tshuaj xyuas ntxiv, xws li siv logarithms ntawm cov ntaub ntawv nrog skewness siab.
Kurtosis (Kev Taw Qhia)
Kev txhais ntawm Kurtosis
Kurtosis yog qhov ntsuas qhov siab thiab qhov ntse ntawm cov ncov ntawm kev faib cov ntaub ntawv. Qhov no txhais tau tias kurtosis cuam tshuam nrog ntau npaum li cas ntawm cov ntaub ntawv nyob hauv cov tails piv rau cov ntaub ntawv ze ntawm qhov nruab nrab. Kurtosis pab txheeb xyuas seb cov ntaub ntawv puas muaj cov tails rog lossis sib dua piv rau kev faib tawm ib txwm muaj.
Hom Kurtosis
1. Leptokurtic: Ib qho kev faib tawm uas muaj lub ncov siab dua thiab cov tw hnyav dua li qhov kev faib tawm ib txwm muaj. Tus nqi kurtosis ntau dua 3. Cov ntaub ntawv nrog kev faib tawm leptokurtic feem ntau muaj cov outliers tseem ceeb dua.
2. Mesokurtic: Ib qho kev faib tawm uas muaj cov yam ntxwv zoo ib yam li qhov kev faib tawm ib txwm muaj. Tus nqi kurtosis yog 3. Qhov kev faib tawm ib txwm muaj nws tus kheej yog ib qho piv txwv ntawm mesokurtic.
3. Platykurtic: Ib qho kev faib tawm uas muaj lub ncov qis dua thiab cov tw sib dua piv rau qhov kev faib tawm ib txwm muaj. Tus nqi kurtosis tsawg dua 3. Ib qho kev faib tawm platykurtic qhia tias cov ntaub ntawv tau faib sib npaug ntau dua thoob plaws ntau yam nqi.
Yuav Ua Li Cas Xam Kurtosis
Kurtosis tuaj yeem suav nrog siv cov qauv hauv qab no:
\[ \text{Kurtosis} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum \left( \frac{x_i – \bar{x}}{s} \right)^4 – \frac{3(n-1)^2}{(n-2)(n-3)} \]
Qhov twg:
– \( n \) = tus naj npawb ntawm cov ntaub ntawv,
– \( x_i \) = tus nqi ntawm tus kheej,
– \( \bar{x} \) = qhov nruab nrab ntawm cov ntaub ntawv,
-\( s\) = qhov sib txawv ntawm tus qauv.
Feem ntau, kurtosis feem ntau hu ua 'kev tshaj kurtosis'. Rau qhov yooj yim, cov mis no feem ntau raug txo los ntawm 3 kom ntseeg tau tias qhov kev faib tawm ib txwm muaj kurtosis ntawm 0.
Kev txhais lus ntawm Kurtosis
Tus nqi kurtosis muab kev nkag siab txog qhov xwm txheej ntawm kev faib cov ntaub ntawv:
- Qhov kurtosis siab qhia txog cov ncov siab thiab cov tw hnyav.
- Qhov kurtosis qis qhia txog kev faib tawm tiaj tus thiab cov tw sib dua.
Qhov Tseem Ceeb ntawm Kurtosis hauv Kev Tshawb Fawb Txog Cov Ntaub Ntawv
Kev nkag siab txog kurtosis pab txheeb xyuas cov outliers thiab npaj cov ntaub ntawv rau kev tshuaj xyuas ntxiv. Piv txwv li, cov ntaub ntawv uas muaj kurtosis siab yuav xav tau cov txheej txheem ruaj khov los tswj cov outliers ntau dhau.
Kev siv tswv yim
1. Nyiaj Txiag: Hauv kev lag luam nyiaj txiag, cov tub ua lag luam siv skewness thiab kurtosis los ntsuas qhov kev pheej hmoo thiab kev ua tau zoo ntawm cov cuab tam. Cov khoom lag luam uas muaj skewness tsis zoo siab yuav qhia txog kev pheej hmoo ntawm kev poob loj heev.
2. Kev Noj Qab Haus Huv Pej Xeem: Hauv kev tshawb fawb txog kab mob sib kis, kev faib cov ntaub ntawv feem ntau tsis yog ib txwm muaj. Skewness thiab kurtosis pab hloov cov ntaub ntawv kom nws siv tau rau hauv cov qauv regression lossis lwm yam kev tshuaj xyuas.
3. Kev Tswj Xyuas Zoo: Cov lag luam tsim khoom feem ntau siv qhov tsis sib xws thiab qhov tsis sib xws los tswj cov khoom zoo. Qhov tsis sib xws siab hauv cov ntaub ntawv tsim khoom yuav qhia txog teeb meem hauv cov txheej txheem tsim khoom.
Xaus
Skewness thiab kurtosis yog ob qho tseem ceeb piav qhia txog kev txheeb cais hauv kev tshuaj xyuas cov ntaub ntawv faib tawm. Skewness muab kev nkag siab txog qhov tsis sib xws ntawm kev faib tawm, thaum kurtosis qhia txog qhov ntse thiab qhov hnyav ntawm cov tw ntawm kev faib tawm. Kev nkag siab txog ob lub tswv yim no muab cov kws tshawb fawb thiab cov kws tshuaj xyuas cov ntaub ntawv nrog cov cuab yeej ntxiv los txhais cov ntaub ntawv kom raug dua thiab txiav txim siab zoo dua hauv ntau yam kev siv.
