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© BrainMass Inc. brainmass.com June 4, 2020, 1:26 am ad1c9bdddf
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.