On the Exact Distribution of Geary’s U-Statistic and its Application to Least Squares Regression

N. N. Mikhail and L. P. Lester
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N. N. Mikhail: Liberty Baptist College
L. P. Lester: Liberty Baptist College

A chapter in Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, 1981, pp 332-335 from Springer

Abstract: Abstract In this paper the first four moments of U-Statistic are derived, to which a two-moment graduation shows that neither a beta distribution nor a scalar multiple chi-square distribution is a good fit to the actual distribution of U-Statistic. On the other hand, a two moment graduation using the exact four moments of U2-Statistic as a scalar multiple chi-square distribution is a very good approximation to the actual distribution of U2-Statistic. A comparison of our results with Gastwirth and Selwyn’s (1980, 139) results are given. From the computations of β1 and β2 for the fitted scalar multiple chi-square and for the actual distribution, we can recommend the fitted scalar multiple chi-square distribution for any statistical tests in practical situations.

Keywords: Proportions; moments; chi-square distribution; sample; population (search for similar items in EconPapers)
Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-9464-8_52

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DOI: 10.1007/978-1-4613-9464-8_52

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