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ⓘ Sebaran Wishart




                                     

ⓘ Sebaran Wishart

Dina statistik, sebaran Wishart, ngaran keur ngahargaan ka John Wishart, salah sahiji kulawarga probability distribution keur nonnegative-definite nilai-matrix variabel random, dihartikeun di handap ieu. Anggap

X 1 ∼ N p 0, V, {\displaystyle X_{1}\sim N_{p}0,V,}

dina hal ieu X 1 nyaéta p ×1 nilai-vektor-kolom variabel random "vektor random" nu mangrupa sebaran normal, nu mana nilai ekspektasi nyaéta p ×1 vektor kolom nu asup sakabéhna nol, sarta varian nyaéta p × p matrik nonnegative definite V. Urang mibanda

E X = μ {\displaystyle EX=\mu }

jeung

var X = E X − μ X − μ ′) = V {\displaystyle {\mbox{var}}X=EX-\muX-\mu)=V}

di mana unggal transpose matrik A dilambangkeun A ′.

Saterusna tempo X 1., X n mangrupa independent and identically distributed. Saterusna sebaran Wishart nyaéta probability distribution tina matrik random p × p

S = ∑ i = 1 n X i X i ′. {\displaystyle S=\sum _{i=1}^{n}X_{i}X_{i}.}

Salah sahiji yén S mibanda sebaran probabiliti dituliskeun ku

S ∼ W p V, n. {\displaystyle S\sim W_{p}V,n.}

Integer positip n mangrupa angka tingkat kabebasan.

Lamun p = 1 jeung V = 1 mangka ieu sebaran mangrupa sebaran chi-kuadrat.

Sebaran Wishart sering dipaké likelihood-ratio test dina analisa multivariate statistik.

                                     
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  • geneticist Sir Ronald Fisher and the statistician John Wishart eponym of the Sebaran Wishart The historian Stephen Stigler has said that the name cumulant
  • Triangular distribution Weibull distribution Wigner semicircle distribution Wishart distribution Zeta distribution Infinite divisibility Indecomposable distribution

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