## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 29, Number 1 (1958), 235-244.

### On Selecting a Subset Which Contains All Populations Better Than a Standard

Shanti S. Gupta and Milton Sobel

#### Abstract

A procedure is given for selecting a subset such that the probability that all the populations better than the standard are included in the subset is equal to or greater than a predetermined number $P^{\ast}$. Section 3 deals with the problem of the location parameter for the normal distribution with known and unknown variance. Section 4 deals with the scale parameter problem for the normal distribution with known and unknown mean as well as the chi-square distribution. Section 5 deals with binomial distributions where the parameter of interest is the probability of failure on a single trial. In each of the above cases the case of known standard and unknown standard are treated separately. Tables are available for some problems; in other problems transformations are used such that the given tables are again appropriate.

#### Article information

**Source**

Ann. Math. Statist., Volume 29, Number 1 (1958), 235-244.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706721

**Digital Object Identifier**

doi:10.1214/aoms/1177706721

**Mathematical Reviews number (MathSciNet)**

MR93852

**Zentralblatt MATH identifier**

0088.12601

**JSTOR**

links.jstor.org

#### Citation

Gupta, Shanti S.; Sobel, Milton. On Selecting a Subset Which Contains All Populations Better Than a Standard. Ann. Math. Statist. 29 (1958), no. 1, 235--244. doi:10.1214/aoms/1177706721. https://projecteuclid.org/euclid.aoms/1177706721