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

Abstract

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.

Keywords:

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

AMS 2000 Subject Classification:

• Primary: 62F20
• 60E05
• Secondary: 62G30

Acknowledgements

The authors are grateful to the anonymous reviewers for their valuable comments and helpful suggestions that contributed to the quality of the article presentation.