Storage capacity of a dam with gamma type inputs

  • A. M. Mathai


Consider 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 independent gamma distributed variables with different parameters. The exact density is written as a finite sum, in terms of zonal polynomials and in terms of confluent hypergeometric functions. Approximations whenn is large and asymptotic results are also given.

Key words and phrases

Random inputs storage capacity distribution of partial sums exact densities computable representation confluent hypergeometric function of many variables 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Constantine, A. G. (1963). Some non-central distribution problems in multivariate analysis,Ann. Math. Statist.,34, 1270–1285.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Cox, D. R. and Miller, H. D. (1978).The Theory of Stochastic Processes, Chapman and Hall, London.Google Scholar
  3. [3]
    Mathai, A. M. and Saxena, R. K. (1978).The H-function with Applications in Statistics and Other Disciplines, Wiley Halsted, New York.zbMATHGoogle Scholar
  4. [4]
    Prabhu, N. U. (1965).Queues and Inventories, Wiley, New York.zbMATHGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

Authors and Affiliations

  • A. M. Mathai
    • 1
  1. 1.McGill UniversityMontrealCanada

Personalised recommendations