The distribution of the sum of independent gamma random variables

@article{Moschopoulos1985TheDO,
  title={The distribution of the sum of independent gamma random variables},
  author={Panagis G. Moschopoulos},
  journal={Annals of the Institute of Statistical Mathematics},
  year={1985},
  volume={37},
  pages={541-544}
}
  • P. Moschopoulos
  • Published 1 December 1985
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
SummaryThe distribution of the sum ofn independent gamma variates with different parameters is expressed as a single gamma-series whose coefficients are computed by simple recursive relations. 
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References

SHOWING 1-4 OF 4 REFERENCES
Probability Content of Regions Under Spherical Normal Distributions, IV: The Distribution of Homogeneous and Non-Homogeneous Quadratic Functions of Normal Variables
Abstract : The distribution of homogeneous and non-homogeneous quadratic functions of normal variables is presented. In geometrical terms the probability content is evaluated for a fixed ellipsoid of… Expand
SERIES REPRESENTATIONS OF DISTRIBUTIONS OF QUADRATIC FORMS IN NORMAL VARIABLES, I. CENTRAL CASE,
Abstract : The probability density function (pdf) of a positive definite quadratic form in (central or non-central) normal variables can be represented as a series expansion in a number of different… Expand
Storage capacity of a dam with gamma type inputs
SummaryConsider mutually independent inputsX1,...,Xn onn different occasions into a dam or storage facility. The total input isY=X1+...+Xn. This sum is a basic quantity in many types of stochastic… Expand
The H-function with applications in statistics and other disciplines