Accession Number : AD0680018

Title :   APPROXIMATE DISTRIBUTIONS FOR LARGEST AND FOR SMALLEST OF A SET OF INDEPENDENT OBSERVATIONS.

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Walsh,John E.

Report Date : 18 SEP 1968

Pagination or Media Count : 15

Abstract : There is often interest in whether the largest observation of a set of n independent observations is unusually large, or the smallest observation is unusually small. Quite accurate approximate probability expressions can be developed for relations of this kind, even though the distributions for the individual observations can be arbitrarily different and all n = or > 1 are considered. More specifically, let X sub n and X sub l denote the largest and smallest observations, respectively. Approximate expressions are developed for P(X sub n = or < x) and P(X sub l = or < x) that are very accurate if 1 - P(X sub n = or < x) = or < 0.15 and P(X sub l = or < x) = or < 0.15. (Author)

Descriptors :   (*DISTRIBUTION THEORY, SAMPLING), (*STATISTICAL DISTRIBUTIONS, CONFIDENCE LIMITS), APPROXIMATION(MATHEMATICS), LEAST SQUARES METHOD, DECISION THEORY, PROBABILITY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE