The Annals of Mathematical Statistics

Some Exact Results for the Finite Dam

N. U. Prabhu

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Abstract

In the discrete finite dam model due to Moran, the storage process $\{Z_t\}$ is known to be a Markov chain. Stationary distributions of $Z_t$ are obtained for the cases where the release is a unit amount of water per unit time, and the input is of (i) geometric, (ii) negative binomial and (iii) Poisson type. The paper concludes with a discussion of the problem of emptiness in the finite dam and considers the probability that, starting with an arbitrary storage, the dam becomes empty before it overflows.

Article information

Source
Ann. Math. Statist., Volume 29, Number 4 (1958), 1234-1243.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706454

Digital Object Identifier
doi:10.1214/aoms/1177706454

Mathematical Reviews number (MathSciNet)
MR99722

Zentralblatt MATH identifier
0091.32202

JSTOR
links.jstor.org

Citation

Prabhu, N. U. Some Exact Results for the Finite Dam. Ann. Math. Statist. 29 (1958), no. 4, 1234--1243. doi:10.1214/aoms/1177706454. https://projecteuclid.org/euclid.aoms/1177706454


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