# Hw8 - Now check that if X is Pareto with theta=1 and nu=1,...

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Test #3 will be on Wednesday, April 22. Exercise: Find the Fisher information matrix for a k-parameter exponential family with the natural parameter w(theta)=theta. Read Sections 8.1, 8.2.1, 8.3.1 (skip example 8.3.8), 8.3.2, and 10.3.1 (stop at the beginning of example 10.3.4). Do problems 8.3, 8.5, 8.6, 8.15, 8.20. Comment on Problem 8.5(c): There are a few ways you can do this. Here is one. If we set theta=1, the Pareto family becomes a scale family in the parameter nu. Since T is scale invariant, the distribution of T (when theta=1) does not depend on the value of nu. Thus we can also set nu=1 without loss of generality.
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Unformatted text preview: Now check that if X is Pareto with theta=1 and nu=1, then Y=log(X) has an exponential distribution with mean 1. This allows you to find the distribution of log(T) using the memoryless property of the exponential distribution: T = sum[log(Xi) - log(min Xi)] and each of the nonzero terms in this sum has an exponential distribution with mean one. (This is just an informal argument.) Thus log(T) has a gamma(n-1,1) distribution. http://www.stat.fsu.edu/~huffer/mordor/5327/test3_material/ch8.homewor. .. 1 of 1 08/08/2009 7:11 PM...
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## This note was uploaded on 12/15/2011 for the course STAT 5326 taught by Professor Frade during the Fall '10 term at FSU.

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