Accession Number : AD0281908

Title :   APPROXIMATE DISTRIBUTION OF EXTREMES FOR NONSAMPLE CASES,

Corporate Author : SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF

Personal Author(s) : Walsh,John E.

Report Date : 23 JUL 1962

Pagination or Media Count : 11

Abstract : The data are n univariate observations that are not necessarily from continuous populations, from the same population, or independent. The problem is to determine an approximate expression for the distribution of a specified largest (or smallest) order statistic of these observations when they satisfy a type of m-dependence. General expressions are developed that depend on n, the order statistic considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual observations. When the data are continuous and the average of the cdf's satisfies some additional conditions as n increases, the extremes have asymptotic distributions of the forms that occur for the case of a sample. These results may explain why many practical situations have been approximated by extreme-value theory that assumes samples. Also, a basis is furnished for deciding, from the characteristics of the situation, on the suitability of extreme-value methods. (Author)

Descriptors :   *STATISTICAL ANALYSIS, *STATISTICAL DISTRIBUTIONS, PROBABILITY, SEQUENCES(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE