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A Note on the Generalized (Positive) Cauchy Distribution

Published online by Cambridge University Press:  20 November 2018

B. Raja Rao  and
M. L. Garg
B. Raja Rao
Affiliation:
Departments of Biostatistics and Mathematics University of Pittsburgh, Pittsburgh Pennsylvania 15213
M. L. Garg
Affiliation:
Department of Biometrics Temple University School of Medicine, Philadelphia, Pa. 19140
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In this note, a certain generalization of the Cauchy distribution is obtained, using the result of Malik [2].

The generalized gamma distribution having the density

(1)

is introduced by Stacy [1], who studied some of its properties. As remarked by Stacy [1], the familiar gamma, chi, chi-squared, exponential and Weibull distributions are special cases of (1), as are the distributions of certain functions of a normal variable - viz.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 865 - 868
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Stacy, E. W., A generalization of the gamma distribution. Ann. Math. Statist. 33 (1962) 1187–1192.Google Scholar
2. Malik, H. J., Exact distribution of the quotient of independent generalized gamma variables. Canad. Math. Bull. 10 (1967) 463–465.Google Scholar