## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 20, Number 3 (1949), 426-432.

### On the Determination of Optimum Probabilities in Sampling

Morris H. Hansen and William N. Hurwitz

#### Abstract

In a previous paper [2] it was shown that it is sometimes profitable to select sampling units with probability proportionate to size of the unit. This note indicates a method of determining the probabilities of selection which minimize the variance of the sample estimate at a fixed cost. Some approximations that have practical applications are given.

#### Article information

**Source**

Ann. Math. Statist., Volume 20, Number 3 (1949), 426-432.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729994

**Digital Object Identifier**

doi:10.1214/aoms/1177729994

**Mathematical Reviews number (MathSciNet)**

MR30729

**Zentralblatt MATH identifier**

0034.23003

**JSTOR**

links.jstor.org

#### Citation

Hansen, Morris H.; Hurwitz, William N. On the Determination of Optimum Probabilities in Sampling. Ann. Math. Statist. 20 (1949), no. 3, 426--432. doi:10.1214/aoms/1177729994. https://projecteuclid.org/euclid.aoms/1177729994