A locally most powerful unbiased test for the proportion of mixture

Abstract

This paper is concerned with a problem of testing hypotheses about the mixing proportion θ of a mixture of two known distributions. A locally most powerful unbiased (LMPU) test for testing the hypotheses H 0: θ = θ 0 vs. H 1: θ ≠ θ 0 (0 < θ 0 < 1) is derived, the asymptotic power function of the test obtained, and an application given.