Asymptotic distributions of order statistics and record values arising from the class of beta-generated distributions

作者：Barakat H M; Nigm E M^*

来源：Statistics, 2014, 48(5): 1005-1012.

DOI：10.1080/02331888.2013.801975

• asymptotic distributions
• order statistics
• record values
• domain of attraction
• beta distribution
• skew t distribution

In this paper, we show that both the class of beta-generated distributions G(F) and its base distribution F belong to the same domain of maximal (or minimal or upper record value or lower record value) attraction. Moreover, it is shown that the weak convergence of any non-extreme order statistic (central or intermediate order statistic), based on a base distribution F, to a non-degenerate limit type implies the weak convergence of G(F) to a non-degenerate limit type. The relations between the two limit types are deduced.

• 出版日期2014