Likelihood Ratio Tests for Homogeneity in Plural Normal Distributions under Small Sample Sizes

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  • 小サンプルによる複数の正規分布の同等性に関する尤度比検定
  • ショウ サンプル ニヨル フクスウ ノ セイキ ブンプ ノ ドウトウ セイ ニ

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Abstract

This paper deals with the null hypothesis test for the homogeneity of plural normal distributions. The likelihood ratio test is a usual method for such testing. The asymptotic distribution of likelihood ratio test statistics is well known, so we could plan the test based on asymptotic distribution. However, when the sample size is small, the accuracy of asymptotic distribution is not assured. In this paper, we derive the cumulant generating function for the log-likelihood ratio statistics for homogeneity in plural normal distributions. Then we consider approximations of log-likelihood ratio statistics by using the cumulants. Furthermore, we confirm that the proposed approximation is more accurate by simulations.

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