Storage capacity of a dam with gamma type inputs

@article{Mathai1982StorageCO,
  title={Storage capacity of a dam with gamma type inputs},
  author={Arak M. Mathai},
  journal={Annals of the Institute of Statistical Mathematics},
  year={1982},
  volume={34},
  pages={591-597}
}
  • A. M. Mathai
  • Published 1 December 1982
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
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 process problems. The distribution ofY and other aspects connected withY are studied by different authors when the inputs are independently and identically distributed exponential or gamma random variables. In this article explicit exact expressions for the density ofY are given whenX1,...,Xn are… Expand
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References

SHOWING 1-5 OF 5 REFERENCES
Some Non-Central Distribution Problems in Multivariate Analysis
The theory of stochastic processes
This book should be of interest to undergraduate and postgraduate students of probability theory.
The H-function with applications in statistics and other disciplines
Theory of stochastic processes
Queues and Inventories