ANZIAM J.
46 (2004), 265271

Independent nonidentical fiveparameter gammaWeibull variates and their sums


Abstract

GammaWeibull 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 nonidentical 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.

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