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December, 1958 Some Exact Results for the Finite Dam
N. U. Prabhu
Ann. Math. Statist. 29(4): 1234-1243 (December, 1958). DOI: 10.1214/aoms/1177706454


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.


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N. U. Prabhu. "Some Exact Results for the Finite Dam." Ann. Math. Statist. 29 (4) 1234 - 1243, December, 1958.


Published: December, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0091.32202
MathSciNet: MR99722
Digital Object Identifier: 10.1214/aoms/1177706454

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 4 • December, 1958
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