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

In: Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface

Author

Listed:
  • N. N. Mikhail

    (Liberty Baptist College)

  • L. P. Lester

    (Liberty Baptist College)

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.

Suggested Citation

  • N. N. Mikhail & L. P. Lester, 1981. "On the Exact Distribution of Geary’s U-Statistic and its Application to Least Squares Regression," Springer Books, in: William F. Eddy (ed.), Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, pages 332-335, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-9464-8_52
    DOI: 10.1007/978-1-4613-9464-8_52
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