Likelihood Ratio Tests for Homogeneity of Two Normal Distributions under Small Sample Sizes

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  • 小サンプルによる正規母集団分布に関する2標本尤度比検定
  • ショウ サンプル ニヨル セイキ ボシュウダン ブンプ ニ カンスル 2 ヒョ

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Abstract

This paper deals with the null hypothesis test for homogeneity of two normal populations. The likelihood ratio test is a usual method for such a test. It is well-known that the distribution of the log-likelihood ratio statistics as the test statistics in likelihood ratio test is asymptotically explained based on the chi-square distribution with 2 degrees of freedom under the null hypothesis as sample size tends to infinity. Therefore, the null hypothesis test for homogeneity of two normal populations is generally designed based on the asymptotic chi-square distribution. However, when sample size is not sufficiently large, the accuracy of the approximation based on the asymptotic chi-square distribution is not necessarily assured. In this paper, the stochastic properties of the log-likelihood ratio statistics for homogeneity of two normal populations are investigated. Furthermore, we consider the null hypothesis test for homogeneity of two normal populations with high accuracy in the case that sample size is not sufficiently large, that is, small.

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