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    Likelihood Ratio Test of two Beta density

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    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
    https://brainmass.com/statistics/hypothesis-testing/likelihood-ratio-test-beta-densities-400247

    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.

    $2.19

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