GENERALIZED ASYMPTOTES FOR EXTREME VALUE DISTRIBUTIONS.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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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 Walshs 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
- Statistics and Probability