Accession Number : AD0688409

Title :   GENERALIZED ASYMPTOTES FOR EXTREME VALUE DISTRIBUTIONS.

Descriptive Note : Technical rept.,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Anderson,Charles L.

Report Date : 14 MAY 1969

Pagination or Media Count : 32

Abstract : Some new asymptotic forms for extreme value distributions are given. The family of distributions is called the quadratic type of dne. It is shown that the sequence of extreme value distributions from a normal distribution is asymptotically attracted to the quadratic type of dne in a stronger sense, related to Walsh's 'Situation I,' than the sense in which it is attracted to the linear type of dne, or first asymptotic type of extreme value distributions, which consists of all distributions of the form exp(- exp(-aX + b) with a positive. It is also shown that the distribution of the largest value in a sample from a normal population can be approximated rather closely by a distribution in the quadratic type of dne even when the sample size is fairly small. Various senses of asymptotic attraction and asymptotic equivalence for sequences of distribution functions are discussed and compared re normal and Poisson populations. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, *ASYMPTOTIC SERIES), DISTRIBUTION THEORY, DISTRIBUTION FUNCTIONS, IDENTITIES, POLYNOMIALS, POPULATION(MATHEMATICS), SAMPLING, FREQUENCY, EXPONENTIAL FUNCTIONS, PROBABILITY, INTEGRAL TRANSFORMS, RANDOM VARIABLES, STABILITY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE