# Exponential Class of Distributions

Not what you're looking for? Search our solutions OR ask your own Custom question.

7.5.3 Let X1, X2,..,Xn denote a random sample of size n from a distribution with pdf f(x; Ã¨) =Ã¨x^(Ã¨-1), 0<x<1, 0 elsewhere, and Ã¨>0.

Show that the geometric mean (X1X2...Xn)^(1/n) of the sample is a complete sufficeint statistic for Ã¨.

Find the maximum likelihood estimator and observe that it is a function of this geometric mean.

https://brainmass.com/statistics/probability/exponential-class-of-distributions-36732

#### Solution Summary

This solution provides a proof to show that the geometric mean of the sample is a complete sufficient statistic for e. It also finds the maximum likelihood estimator and also shows how it is a function of the geometric mean. All steps are shown with brief explanations.

$2.49