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Comparing Distributions: The Harmonic Mass Index: Extension to m Samples

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Abstract

We extend the paper of Hinloopen and van Marrewijk (2005), who introduce the harmonic mass index to test whether two samples come from the same distribution, in the following directions. Firstly, we derive the Harmonic Weighted Mass (HWM) index for any number of samples. Secondly, this paper shows how to compute the HWM index without making any assumptions on the number of "ties" (i.e. identical observations) within or between samples. Thirdly, we investigate ties with a Monte Carlo analysis, and find that the critical percentiles as reported in Hinloopen and van Marrewijk (2005), for two samples that are free of ties, are fairly accurate approximations of the HWM percentiles for two samples with ties when the sample size exceeds 50 observations. Furthermore, our results show that these percentiles are fairly accurate as well for cases where there are more than two samples.

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  • Wagenvoort, Rien, 2007. "Comparing Distributions: The Harmonic Mass Index: Extension to m Samples," Economic and Financial Reports 2006/3, European Investment Bank, Economics Department.
    • Handle: RePEc:ris:eibefr:2006_003
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    Keywords

    Harmonic mass index; Harmonic weighted mass; Distributions; m samples;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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