## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 27, Number 3 (1956), 670-686.

### A Comparison of Tests on the Mean of a Logarithmico-Normal Distribution with Known Variance

Norman C. Severo and Edwin G. Olds

#### Abstract

Three test procedures are considered for testing an hypothesis on the mean of a logarithmico-normal distribution with known variance. The first is a normal theory test applied to the logarithms of the original data; the second is a normal theory test applied to the original data; and the third is a test based on the Neyman-Pearson Lemma. The operating characteristics of these tests are developed and some asymptotic properties obtained. It is found that the three procedures give quite different results unless the mean under the null hypothesis is large relative to the standard deviation.

#### Article information

**Source**

Ann. Math. Statist., Volume 27, Number 3 (1956), 670-686.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728175

**Digital Object Identifier**

doi:10.1214/aoms/1177728175

**Mathematical Reviews number (MathSciNet)**

MR81603

**Zentralblatt MATH identifier**

0073.14402

**JSTOR**

links.jstor.org

#### Citation

Severo, Norman C.; Olds, Edwin G. A Comparison of Tests on the Mean of a Logarithmico-Normal Distribution with Known Variance. Ann. Math. Statist. 27 (1956), no. 3, 670--686. doi:10.1214/aoms/1177728175. https://projecteuclid.org/euclid.aoms/1177728175