Limit theory of bivariate dual generalized order statistics with random index

ABSTRACT

The class of limit distribution functions of bivariate extreme, intermediate and central dual generalized order statistics from independent and identically distributed random variables with random sample size is fully characterized. Two cases are considered. The first case is when the random sample size is assumed to be independent of all basic random variables. The second case is when the interrelation of the random size and the basic random variables is not restricted.

KEYWORDS:

• Weak convergence
• sample of random size
• bivariate dual generalized order statistics

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62E20
• Secondary: 62E15
• 62G30

Acknowledgements

The authors are immensely grateful to the chief editor, Professor Meister, and the associated editor, as well as the anonymous referees for their careful reading of the manuscript and their critical and useful comments, from which the paper has benefited a lot.

Disclosure statement

No potential conflict of interest was reported by the authors.