The Annals of Mathematical Statistics

Some Exact Results for the Finite Dam

N. U. Prabhu

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

First available in Project Euclid: 27 April 2007

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

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