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A rank test based on the moments of order statistics of the modified Makeham distribution

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Abstract

Single moments of order statistics from the modified Makeham distribution (MMD) are derived, an identity about the single moments of order statistics is given, and the specific expected value and variance of the single moments of order statistics from the MMD are calculated. In this study, the order statistic from the MMD was applied to the rank sum test in a two-sample problem. The exact critical values of the designated statistics were evaluated. Simulations were used to investigate the power of these statistics for the two-sided alternative with several population distributions. The powers of the statistics were compared with the Wilcoxon rank sum statistic, the Lepage statistic, the modified Baumgartner statistic, the Savage test and the normal score test. The Edgeworth expansion was used to evaluate the upper tail probability for the preferred statistic, given finite sample sizes.

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Acknowledgments

The authors would like to thank the editor and the two referees for their valuable comments and suggestions. The author also appreciates that this research is supported by the Grant-in-Aid for Young Scientists B of JSPS, KAKENHI Numbers 23700349 and 26730025.

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Authors and Affiliations

  1. Clinical Research Support Center, Mie University Hospital, Tsu, Mie, Japan

    T. Ogura

  2. Department of Mathematics, National Defense Academy, Yokosuka, Kanagawa, Japan

    H. Murakami

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  1. T. Ogura
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  2. H. Murakami
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Correspondence to T. Ogura.

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Ogura, T., Murakami, H. A rank test based on the moments of order statistics of the modified Makeham distribution. Comput Stat 29, 1691–1711 (2014). https://doi.org/10.1007/s00180-014-0513-2

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  • DOI: https://doi.org/10.1007/s00180-014-0513-2

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