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The modified Mood test for the scale alternative and its numerical comparisons

Authors
Murakami, HidetoshiHa, Hyung-Tae
Issue Date
Dec-2015
Publisher
KOREAN STATISTICAL SOC
Keywords
Approximation; Critical values; Asymptotic efficiency; Modified Mood test; Power comparison
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.44, no.4, pp.592 - 605
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
44
Number
4
Start Page
592
End Page
605
URI
https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/9880
DOI
10.1016/j.jkss.2015.03.005
ISSN
1226-3192
Abstract
On statistical hypotheses testing in two-sample problems, the Mood test is popular as one of the most efficient nonparametric tests for dispersion differences. In this paper, we show that a modification of the Mood test proposed by Tamura (1963) can gain even more efficiency and power under various distributional assumptions. The accuracy of the proposed approximations to the tail probabilities and critical values of the modified Mood test, namely M-p, were investigated. Our results showed that the Edgeworth expansion was more accurate than the other approximations. Asymptotic efficiencies and the optimal value p of the modified Mood test under various distributional assumptions were examined, with the results revealing that the large (small) value of p was useful for light (heavy) tail distributions. Additionally, the power of the modified Mood test for the one-sided alternative with various population distributions for small sample sizes was investigated via Monte Carlo simulations. Finally, the proposed method was demonstrated using real data. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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Social Sciences (Department of Applied Statistics)
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