# Accession Number:

## AD0680435

# Title:

## SAMPLE SIZE REQUIRED TO ESTIMATE A PARAMETER IN THE POWER FUNCTION DISTRIBUTION,

# Descriptive Note:

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1968-09-25

# Pagination or Media Count:

## 11.0

# Abstract:

The purpose of the paper is to establish a two step sampling procedure for estimating the parameter theta of the power function distribution to within given d units of its true value with a given probability 1 - alpha 0 alpha 1. The density of the power function distribution is a function of two parameters, the second of which k is assumed known. It is demonstrated that an exact solution for all values of theta does not exist based on the maximum likelihood estimator. Given a preliminary sample size m, tables and formulas are presented by which one may establish the size n of the second sample such that Pabsolute value of y sub n - theta d 1 - alpha is true, where y sub n is the largest observation in the second sample. The method used in deriving the results of this paper is similar to that given by Graybill and Connell and since the power function density reduces to the uniform density when k 0, their results can be derived from the formulas given here. Also a table of comparisons between the expected second sample size in this paper and two other solutions is given. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability