## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 29, Number 2 (1958), 571-575.

### Probabilities of Hypotheses and Information-Statistics in Sampling from Exponential-Class Populations

#### Abstract

This paper is concerned with inequalities connecting probabilities of hypotheses using Bayes' theorem (a posteriori probabilities), a priori probabilities, and Kullback-Leibler information-statistics in sampling from populations belonging to the exponential class of populations. As a corollary, it is shown that if it is known that the a priori probabilities are all equal, the choice of the hypothesis with the minimum Kullback-Leibler information-statistic is the same as the choice of the hypothesis with the maximum a posteriori probability, and conversely.

#### Article information

**Source**

Ann. Math. Statist., Volume 29, Number 2 (1958), 571-575.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706633

**Digital Object Identifier**

doi:10.1214/aoms/1177706633

**Mathematical Reviews number (MathSciNet)**

MR100937

**Zentralblatt MATH identifier**

0087.14402

**JSTOR**

links.jstor.org

#### Citation

Kupperman, Morton. Probabilities of Hypotheses and Information-Statistics in Sampling from Exponential-Class Populations. Ann. Math. Statist. 29 (1958), no. 2, 571--575. doi:10.1214/aoms/1177706633. https://projecteuclid.org/euclid.aoms/1177706633

#### Corrections

- See Correction: Morton Kupperman. Correction to "Probabilities of Hypotheses and Information-Statistics in Sampling From Exponential-Class Populations". Ann. Math. Statist., Vol. 29, Iss. 4 (1958) 1278.Project Euclid: euclid.aoms/1177706462