(untitled) (Statistics, Optimization & Information Computing, 2025)
In this paper, we employ generalized order statistics to investigate the moment properties of the Benktander Type II distribution. Through this approach, we derive precise and explicit formulas for single moments and establish recurrence relations for single and product moments. Additionally, we present a characterization of the Benktander Type II distribution, accompanied by further implications regarding moments of record values and ordinary order statistics. We estimate the unknown parameters of the Benktander Type II distribution using Maximum Likelihood (ML) estimation for generalized order statistics (gos). Subsequently, we conduct simulation studies encompassing order statistics. The efficacy of the obtained ML estimates is evaluated through comprehensive simulation analyses, focusing on various moments and their relative mean squared errors. This research contributes to understanding the Benktander Type II distribution’s properties and provides valuable insights into its parameter estimation using generalized order statistics.