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  4. Order Statistics and Extremes

Order Statistics and Extremes

Colección

We introduce the order statistics of a sample and the special order statistics minimum and maximum of the sample. We show how to obtain the joint distribution of any subset of order statistics, that includes the maximum, minimum and any particular order statistic or any subset of order statistics

Autores Enrique Castillo
Fecha 16/09/2019 Idioma

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Contenido

Order Statistics

 We introduce the concept of order statistics and derive the joint density of any k order statistics. As particular cases, we derive the density of any order statistic, in particular the minimum and the maximum, the joint density of any two order statistics and the joint density of all order statistics. Some illustrative examples are given.

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Limit distributions of extremes

 We study the limit distributions of extremes, minima and maxima, in the case of independence. It is shown that a unique family of distributions is possible for minima and another one for maxima. This family can be partitioned into the well known Weibull, Gumbel and Frechet fmilies of distributions. Some materials to work with extremes is given to the users.

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