## The Annals of Mathematical Statistics

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

### Some Exact Results for the Finite Dam

#### 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