Moment Properties of Generalized Order Statistics Based on Modified Weighted Rayleigh Distribution

Abstract

The generalized order statistics is a unified model of several ordered random schemes such as order statistics, record values, progressive type II right censored order statistics, etc. Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. Progressive Type-II censored sampling scheme is a versatile censoring scheme because it allows the experimenter to save time and cost of the life-testing experiment and is quite useful in reliability and lifetime studies. Rayleigh distribution and its extended version such as modified weighted Rayleigh distribution are important distributions for modeling lifetime data in reliability analysis and engineering science. In this paper, we studied moment properties of generalized order statistics from modified weighted Rayleigh distribution. Further, characterization results based on moment properties and conditional expectation are presented. The simulation studies based on order statistics, upper record values, and progressive type II right censored order statistics are also carried out.