Log-Extended Exponential–Geometric Distribution: Moments and Inference Based on Generalized Order Statistics

Abstract

In this paper, we provide explicit expressions as well as recurrence relations for the single and product moments of generalized order statistics from the log-extended exponential–geometric distribution. These relations are utilized to discuss the special cases of generalized order statistics, and some numerical computations are carried out. Further, we use these results to obtain the best linear unbiased estimators for the location and scale parameters based on progressively Type-II right censored samples. Finally, a real data application is presented.

Keywords

• best linear unbiased estimators
• generalized order statistics
• log-extended exponential–geometric distribution
• product moments
• recurrence relations
• single moments