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Exact Distribution of the Quotient of Independent Generalized Gamma Variables

Published online by Cambridge University Press:  20 November 2018

Henrick John Malik
Henrick John Malik*
Affiliation:
Department of National DefenceRoyal Roads Canadian Services CollegeVictoria, B. C.
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Let X be a random variable whose frequency function is

1.1

Form (1.1) is Stacy′s [3] generalization of the gamma distribution. The familiar gamma, chi, chi-squared, exponential and Weibull variâtes are special cases, as are certain functions of normal variate - viz., its positive even powers, its modulus, and all positive powers of its modulus.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 463 - 465
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Amorose, L., Ricercheintorno alia curva dei redditi. Ann. Mat. Pura Appl. Series 4, 21, pp. 123-150.Google Scholar
2. Kendall, M. G. and Stuart, A., The Advanced Theory of Statistics, Volume 1, Hafner Publishing Company, New York, 1948.Google Scholar
3. Stacy, E. W., A generalization of the gamma distribution. Annals of Mathematical Statistics. Volume 33 (1966), 1187-1192.Google Scholar
4. Whittaker, and Watson, , Modern Analysis. Second edition, p. 283.Google Scholar