ANZIAM  J.  46 (2004), 265-271
Independent non-identical five-parameter gamma-Weibull variates and their sums

Roy B. Leipnik
  Mathematics Department
  Ca 93106--3080
Charles E. M. Pearce
  School of Mathematics
  The University of Adelaide
  SA 5005

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.
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