## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 37, Number 4 (1966), 940-944.

### On the Pitman Efficiency of One-sided Kolmogorov and Smirnov Tests for Normal Alternatives

#### Abstract

Lower bounds for the Pitman efficiency of the one-sided Kolmogorov test for all normal alternatives and for the Smirnov test for normal shift alternatives are obtained. In the one-sample case this does not fall below 36 per cent at the usual levels of significance and power. In the two-sample case the lower bound depends on the ratio of the two sample sizes and does not fall below 36 per cent when the ratio is larger than 40. We assume that the results of [1] are known.

#### Article information

**Source**

Ann. Math. Statist., Volume 37, Number 4 (1966), 940-944.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177699374

**Digital Object Identifier**

doi:10.1214/aoms/1177699374

**Mathematical Reviews number (MathSciNet)**

MR193710

**Zentralblatt MATH identifier**

0144.19202

**JSTOR**

links.jstor.org

#### Citation

Ramachandramurty, P. V. On the Pitman Efficiency of One-sided Kolmogorov and Smirnov Tests for Normal Alternatives. Ann. Math. Statist. 37 (1966), no. 4, 940--944. doi:10.1214/aoms/1177699374. https://projecteuclid.org/euclid.aoms/1177699374