Pearson txoj cai faib khoom yog dab tsi? Cov lus teb rau lo lus nug dav no tsis tuaj yeem yooj yim thiab luv. Lub Pearson system yog thawj zaug tsim los ua qauv pom qhov txawv txav. Thaum lub sijhawm, nws tau paub zoo tias yuav kho tus qauv theoretical li cas kom haum rau thawj ob qhov kev sib tw lossis lub sijhawm ntawm cov ntaub ntawv pom: txhua qhov kev faib tawm yuav raug nthuav tawm ncaj qha los tsim ib pawg ntawm qhov chaw teev.
Pearson qhov kev xav txog qhov kev faib tawm ntawm cov qauv
Tshwj tsis yog nyob rau hauv cov xwm txheej pathological, qhov ntsuas qhov chaw tuaj yeem ua kom haum rau qhov pom tau tias (thawj cumulant) thiab qhov sib txawv (thib ob cumulant) hauv ib qho kev txiav txim siab. Txawm li cas los xij, nws tsis paub yuav ua li cas thiaj tsim tau qhov kev faib tawm uas skewness (tus qauv thib peb cumulant) thiab kurtosis (tus qauv thib plaub cumulant) tuaj yeem tswj tau sib npaug. Qhov kev xav tau no tau tshwm sim thaum sim ua kom haum cov qauv theoretical paub txog cov ntaub ntawv pom,leej twg pom asymmetry.
Nyob hauv video hauv qab no koj tuaj yeem pom kev tsom xam ntawm Pearson's chi-distribution.
History
Nyob hauv nws txoj haujlwm qub, Pearson tau txheeb xyuas plaub hom kev faib tawm (tus lej I txog IV) ntxiv rau qhov kev faib tawm ib txwm (uas yog thawj lub npe hu ua hom V). Kev faib tawm yog nyob ntawm seb qhov kev faib khoom tau txais kev txhawb nqa dhau ib ntus, ntawm ib nrab-axis, lossis ntawm tag nrho cov kab tiag tiag, thiab seb lawv puas muaj peev xwm skewed lossis yuav tsum sib npaug.
Ob qhov kev tsis lees paub tau raug kho nyob rau hauv daim ntawv thib ob: nws rov txhais hom V kev faib tawm (thaum pib nws tsuas yog kev faib tawm ib txwm, tab sis tam sim no nrog inverse gamma) thiab qhia hom VI faib. Ua ke, thawj ob kab lus hais txog tsib yam tseem ceeb ntawm Pearson system (I, III, IV, V, thiab VI). Nyob rau hauv daim ntawv thib peb, Pearson (1916) tau qhia ntxiv subtypes.
Txhim kho lub tswvyim
Rind tau tsim ib txoj hauv kev yooj yim kom pom qhov tsis muaj qhov chaw ntawm Pearson system (lossis faib cov qauv), uas nws tom qab tau txais. Niaj hnub no, ntau tus lej thiab cov lej suav siv cov qauv no. Hom Pearson distributions yog tus cwj pwm los ntawm ob qhov ntau, feem ntau hu ua β1 thiab β2. Thawj yog lub square ntawm asymmetry. Qhov thib ob yog cov tsoos kurtosis, lossis lub sijhawm thib plaub tus qauv: β2=γ2 + 3.
Txoj kev lej niaj hnub txhais kurtosis γ2 ua cov cumulants tsis yog lub sijhawm, yog li rau qhov qubfaib peb muaj γ2=0 thiab β2=3. Ntawm no nws yog tsim nyog ua raws li keeb kwm precedent thiab siv β2. Daim duab ntawm sab xis qhia tau hais tias hom twg yog qhov tshwj xeeb Pearson kev faib tawm yog (tus cim los ntawm qhov teev (β1, β2).
Ntau yam ntawm skewed thiab/los yog tsis-mesokurtic distributions peb paub niaj hnub no tseem tsis tau paub nyob rau hauv thaum ntxov 1890s. Tam sim no lub npe hu ua qhov kev faib tawm beta tau siv los ntawm Thomas Bayes raws li qhov ntsuas tom qab ntawm Bernoulli kev faib tawm hauv nws daim ntawv 1763 ntawm qhov tshwm sim rov qab.
Kev faib tawm beta tau nce siab vim nws muaj nyob hauv Pearson system thiab tau paub txog thaum xyoo 1940 raws li Pearson yam kuv faib. Kev faib tawm Hom II yog qhov tshwj xeeb ntawm Hom I, tab sis feem ntau nws tsis raug cais tawm lawm.
Kev faib khoom Gamma yog los ntawm nws tus kheej ua haujlwm thiab paub tias yog Pearson Hom III Ib txwm faib ua ntej nws tau txais nws lub npe niaj hnub hauv xyoo 1930 thiab 1940s. Ib daim ntawv xyoo 1895 los ntawm ib tus kws tshawb fawb tau nthuav tawm Hom IV kev faib tawm, uas muaj Cov Tub Ntxhais Kawm T-kev faib tawm, uas yog qhov tshwj xeeb, ua rau William Seely Gosset siv tom qab siv ntau xyoo. Nws daim ntawv 1901 tau nthuav tawm kev faib khoom nrog inverse gamma (hom V) thiab beta primes (hom VI).
Ib qho kev xav
Kojraws li Ord, Pearson tsim kho cov qauv sib npaug (1) raws li cov qauv ntawm cov kev faib tawm ib txwm muaj (uas muab txoj kev faib tawm ntawm txoj kev faib tawmqauv). Ntau tus kws tshaj lij tseem koom nrog hauv kev sim cov kev xav txog kev faib tawm ntawm Pearson cov qauv. Thiab nws ua pov thawj nws cov txiaj ntsig.
Leej twg yog Karl Pearson
Karl Pearson yog ib tus kws lej Askiv thiab biostatistician. Nws tau txais txiaj ntsig los ntawm kev tsim cov kev qhuab qhia ntawm lej txheeb cais. Xyoo 1911 nws tau tsim lub ntiaj teb thawj chav haujlwm ntawm kev txheeb cais ntawm University College London thiab ua haujlwm tseem ceeb rau thaj chaw ntawm biometrics thiab huab cua. Pearson kuj yog tus txhawb nqa ntawm kev sib raug zoo Darwinism thiab eugenics. Nws yog Sir Francis G alton tus protégé thiab biography.
Biometrics
Karl Pearson yog qhov tseem ceeb hauv kev tsim lub tsev kawm ntawv ntawm biometrics, uas yog kev sib tw txoj kev xav piav qhia txog kev hloov pauv thiab qub txeeg qub teg ntawm cov pej xeem thaum tig ntawm lub xyoo pua 20th. Nws series ntawm kaum yim cov ntaub ntawv "Kev Ua lej Ua lej rau Txoj Cai ntawm Evolution" tau tsim nws los ua tus tsim ntawm lub tsev kawm ntawv biometric ntawm qub txeeg qub teg. Qhov tseeb Pearson tau mob siab rau nws lub sijhawm ntau thaum xyoo 1893-1904 rau txoj kev loj hlob ntawm statistical txoj kev rau biometrics. Cov txheej txheem no, uas tau siv dav niaj hnub no rau kev txheeb xyuas kev txheeb xyuas, suav nrog kev ntsuas chi-square, tus qauv sib txawv, kev sib raug zoo thiab cov coefficients regression.
xov xwm ntawm noob neej
Pearson txoj cai ntawm kev yug me nyuam tau hais tias cov kab mob plasm muaj cov khoom qub los ntawm cov niam txiv, nrog rau cov poj koob yawm txwv nyob deb, qhov feem ntawm qhov sib txawv raws li ntau yam ntxwv. Karl Pearson yog ib tug thwjtim ntawm G alton, thiab txawm tias lawvCov hauj lwm txawv ntawm qee qhov kev hwm, Pearson siv ntau qhov tseem ceeb ntawm nws tus kws qhia ntawv cov ntsiab lus hauv kev tsim lub tsev kawm ntawv biometric rau qub txeeg qub teg, xws li txoj cai ntawm kev thim rov qab.
Tsev kawm nta
Lub tsev kawm ntawv biometric, tsis zoo li Mendelians, tsis yog tsom rau kev muab cov txheej txheem rau kev ua qub txeeg qub teg, tab sis ntawm kev muab cov lus piav qhia lej uas tsis yog qhov tshwm sim. Thaum G alton tau tshaj tawm txoj kev xav tsis tu ncua ntawm evolution nyob rau hauv uas hom yuav hloov pauv loj leaps ntau dua li cov kev hloov pauv me me uas tau sau dhau sijhawm, Pearson tau taw qhia qhov tsis zoo hauv qhov kev sib cav no thiab siv nws lub tswv yim los tsim txoj kev xav tsis tu ncua ntawm evolution. Cov Mendelians nyiam qhov kev xav tsis tu ncua ntawm evolution.
Thaum G alton tau tsom mus rau qhov tseem ceeb ntawm kev siv cov txheej txheem txheeb cais rau kev kawm txog kev xeeb tub, Pearson thiab nws cov npoj yaig Weldon nthuav dav lawv qhov laj thawj hauv cheeb tsam no, kev hloov pauv, kev sib raug zoo ntawm kev xaiv ntuj thiab kev sib deev.
Saib ntawm evolution
Rau Pearson, txoj kev xav ntawm evolution tsis yog tsim los txheeb xyuas cov txheej txheem lom neeg uas piav qhia txog cov qauv ntawm kev qub txeeg qub teg, thaum Mendelian txoj hauv kev tshaj tawm cov noob los ua cov txheej txheem ntawm kev qub txeeg qub teg.
Pearson thuam Bateson thiab lwm tus kws kho tsiaj txog tsiaj txhu tsis tau siv cov txheej txheem biometric hauv lawv txoj kev kawm txog evolution. Nws rau txim rau cov kws tshawb fawb uas tsis tsom ntsoov raustatistical validity ntawm lawv txoj kev xav, hais tias:
"Ua ntej peb tuaj yeem lees txais [txhua qhov ua rau muaj kev hloov pauv hloov pauv] ua qhov tseem ceeb, peb yuav tsum tsis yog qhia nws qhov kev cia siab xwb, tab sis, yog tias ua tau, ua kom pom nws qhov peev xwm ntau."
Biologists tau ua tiav rau "yuav luag qhov kev xav ntawm metaphysical txog qhov ua rau muaj kev xeeb tub" uas tau hloov cov txheej txheem ntawm kev sau cov ntaub ntawv sim, uas tuaj yeem tso cai rau cov kws tshawb fawb kom txo qis qhov muaj peev xwm theories.
Laws of nature
Rau Pearson, cov kev cai ntawm xwm tau muaj txiaj ntsig zoo rau kev kwv yees kom raug thiab rau cov ntsiab lus sib txawv hauv cov ntaub ntawv pom. Yog vim li cas yog qhov kev paub "tias ib ntus tshwm sim thiab rov ua dua yav dhau los."
Yog li, txheeb xyuas cov txheej txheem tshwj xeeb ntawm cov noob caj noob ces tsis yog qhov tsim nyog rau kev sim rau biologists, uas yuav tsum tau tsom mus rau kev piav qhia lej ntawm cov ntaub ntawv empirical. Qhov no ib nrab ua rau muaj kev tsis sib haum xeeb ntawm biometrists thiab Mendelians, suav nrog Bateson.
Tom qab tom qab tsis lees paub ib qho ntawm Pearson cov ntawv sau piav qhia txog kev xav tshiab ntawm cov xeeb ntxwv hloov pauv lossis homotypy, Pearson thiab Weldon tau tsim lub tuam txhab Biometrika xyoo 1902. Txawm hais tias txoj hauv kev biometric mus rau qhov qub txeeg qub teg thaum kawg poob nws qhov kev xav ntawm Mendelian, cov txheej txheem uas lawv tsim thaum lub sijhawm tseem ceeb heev rau kev kawm txog biology thiab evolution niaj hnub no.
