## The Annals of Mathematical Statistics

### Some Exact Results for the Finite Dam

N. U. Prabhu

#### 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

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