# Likelihood Ratio Test of two Beta density

Suppose that X1, X2, ..., Xn are iid with a beta (nu,1) distribution and Y1, Y2, ..., Ym are iid beta (theta, 1) distribution. Assume Xs and Ys are independent.

1) FInd a likelihood ratio test of Ho: theta = nu vs. Ha: theta different from nu

2) Show that the test in part A can be based on the statistic

T = (sum of log(Xi))/((sum of log(Xi))+(sum of log(Yi)))

3) Find the distribution of the test statistic when the null hypothesis is true, and then show how to get a test size alpha= 0.10

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#### Solution Summary

In this solution, we obtain a likelihood ratio test for testing whether two beta densities are equal. Additionally, we find the distribution of the test statistic when the null hypothesis is true.

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