# Storage capacity of a dam with gamma type inputs

## Authors

- Received:

DOI: 10.1007/BF02481056

- Cite this article as:
- Mathai, A.M. Ann Inst Stat Math (1982) 34: 591. doi:10.1007/BF02481056

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## Summary

Consider mutually independent inputs*X*_{1},...,*X*_{n} on*n* different occasions into a dam or storage facility. The total input is*Y*=*X*_{1}+...+*X*_{n}. This sum is a basic quantity in many types of stochastic process problems. The distribution of*Y* and other aspects connected with*Y* 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 of*Y* are given when*X*_{1},...,*X*_{n} 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 when*n* is large and asymptotic results are also given.