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On a distribution of Leipnik and Pearce

Published online by Cambridge University Press:  17 February 2009

Saralees Nadarajah  and
Samuel Kotz
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Abstract

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A recent paper by Leipnik and Pearce introduced the gamma Weibull distribution. One of the main properties given is its characteristic function, which is expressed as an infinite sum. In this note, we provide a simpler representation in terms of the well-known hypergeometric functions in some special cases. We also derive expressions for moments of the distribution.

Keywords

gamma distributionWeibull distribution.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 405 - 407
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, 6th ed. (Academic Press, San Diego, CA, 2000).Google Scholar
[2]Leipnik, R. B. and Pearce, C. E. M., “Independent non-identical five-parameter gamma-Weibull variates and their sums”, ANZIAM J. 46 (2004) 265–271.CrossRefGoogle Scholar
[3]Prudnikov, A. P., Brychkov, Y. A. and Marichev, O. I., Integrals and Series, Volumes 1, 2 and 3 (Gordon and Breach Science Publishers, Amsterdam, 1986)Google Scholar