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

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  • T. Ogura
  • H. Murakami

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • T. Ogura & H. Murakami, 2014. "A rank test based on the moments of order statistics of the modified Makeham distribution," Computational Statistics, Springer, vol. 29(6), pages 1691-1711, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1691-1711
    DOI: 10.1007/s00180-014-0513-2
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    References listed on IDEAS

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    1. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.
    2. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    3. P. Thomas & Philip Samuel, 2008. "Recurrence relations for the moments of order statistics from a beta distribution," Statistical Papers, Springer, vol. 49(1), pages 139-146, March.
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