E p 1 1 fx x 2 2 2 exp x t 1 x 2 where 1 2 p p

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Unformatted text preview: g the sequence X1 , . . . , Xn . So, the joint pdf of n ordered uniforms is given by fU(1)) ,...,U(n) (u(1) , u(2) , . . . , u(n) ) = n! Hence result. 5.2 Multivariate Normal Distribution Suppose we wish to generate X = ( X1 , . . . , X p ) T ¯ with X ∼ MVNp (µ, Σ) i.e. ¯ ¯ p 1 1 fX (x) = (2π )− 2 |Σ|− 2 exp − (x − µ)T Σ−1 (x − µ) ¯ ¯¯ 2¯ ¯ where, µ= ¯ µ1 µ2 . . . µp Σp×p = (Σij ) Σii = var(Xi ) E(Xi ) = µi Σij = cov(Xi , Xj ) 64 First generate Zi ∼ N(0, 1), i = 1, . . . , p (i...
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This document was uploaded on 03/25/2014.

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