Generalized exponential distribution: Moments of order statistics

Abstract

In this paper, we consider the generalized exponential distribution (GED) with shape parameter α. We establish several recurrence relations satisfied by the single and the product moments for order statistics from the GED. The relationships can be written in terms of polygamma and hypergeometric functions and used in a simple recursive manner in order to compute the single and the product moments of all order statistics for all sample sizes.

Keywords:

• Order statistics
• Moment generating function
• Moments of order statistics
• Polygamma functions
• Hypergeometric functions
• Riemann zeta function

Acknowledgments

The author would like to thank the University of Jordan for supporting this research work. The author also thanks the referee for useful suggestions.