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Independent non-identical five-parameter gamma-Weibull variates and their sums

Published online by Cambridge University Press:  17 February 2009

Roy B. Leipnik  and
Charles E. M. Pearce
Roy B. Leipnik
Affiliation:
Mathematics Department, UCSB, Ca 93106–3080, USA; e-mail: leipnik@math.ucsb.edu.
Charles E. M. Pearce
Affiliation:
School of Mathematics, The University of Adelaide, SA 5005, Australia; e-mail: cpearce@maths.adelaide.edu.au.
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Abstract

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Gamma-Weibull variates with five parameters are defined by multiplication of gamma and Weibull densities and renormalising. Sums of independent such variates are distributed as combinations of products of gammas and confluent hypergeometric functions and are explicitly determined. Sums of independent non-identical Weibulls arise as a special case. These variates can be used to model moderately extreme scenarios between gamma and Weibull that occur in many natural applications. All results are exact.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 2 , October 2004 , pp. 265 - 271
Copyright
Copyright © Australian Mathematical Society 2004

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