Multivariate Analysis-Wishart's Distribution (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 1 of 1

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Question number: 1

» Multivariate Analysis » Wishart's Distribution » Reproductive Properties

Appeared in Year: 2015

Essay Question▾

Describe in Detail

(i) Let A i be distributed as Wishart Equation , i = 1, 2 and A 1, A 2 be independent. Show that A 1 +A 2 is distributed as Equation .

(ii) If A is distributed as Equation , then CAC’ is distributed as Equation where C is a nonsingular matrix of order m.

Explanation

(i) We have Equation that is

Equation where Equation ) and Y i ’s are independent.

Similarly, Equation that is

Equation where Equation ) and Z i ’s are independent.

We know that A 1, A 2 are independent. So, Y i ’s are independent of Z i ’s

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