Two-Sample Tests for Compound Distributions for Homogeneity of Mixing Proportions

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Abstract
This paper is concerned with a problem of comparing two compound distributions each with components f 1(x) and f 2(x), and with mixing proportions px and (1 – px) for the first, and py and (I – py) for the second distribution, respectively. Four methods are proposed for testing the hypothesis Ho :px = py. The first two tests are based on the asymptotic normality of two unbiased estimators for py – px, and the other two are nonparametric tests. The asymptotic power functions for the tests are given and a simulation technique is used to compare the efficiencies of the four tests applied for mixed normal and for mixed exponential distributions.

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