Revisit the Wishart Distributionm

William Chen

International Journal of Statistics and Probability, 2020, vol. 9, issue 5, 79

Abstract: If S_pxp can be written as S=X' X , where X_nxp is a data matrix from N_p(0,V) , then S is said to have a Wishart distribution with scale matrix V of degree of freedom parameter n. We write S~W_p(V,n). When V=I, the distribution is said to be in standard form. When p=1, the W_1(σ^2, n) distribution is found to be Σ^n_i=1(x^2_i) , where the elements of x_i are identically independently distributed unit normal variables; being the σ^2(x_n)^2 distribution. Although Anderson (1984, p248~249) has presented two theorems for the Wishart distribution. In the following we give an alternative proof.

Date: 2020
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