On Moments of Inverse Kumaraswamy Distribution Based on Progressive Type-II Censored Order Statistics

Daghistani et al. (Pak J Stat Oper Res 989–997, 2019) introduced and investigated the properties of the new inverse Kumaraswamy distribution. This distribution has numerous applications in various fields, including life testing, biology, and medicine. Also, it is used in reliability and survival analysis. The progressively Type-II censored sampling method is a versatile censoring technique since it helps the researcher to save cost and time of the life testing experiments, and it is very beneficial in reliability studies. This article provides explicit expressions and recurrence relations between the single and product moments of progressively Type-II right censored order statistics from the inverse Kumaraswamy distribution. Similar results for usual order statistics are also shown as special cases. The means and variances of progressively Type-II right censored order statistics for various parameter values are then calculated using these findings. The best linear unbiased estimators for the location and scale parameters of the inverse Kumaraswamy distribution are also investigated. Further, based on the observed progressively Type-II right censored order statistics, we discuss how to obtain the best linear unbiased predictors for future observations. Finally, we consider a real data set as an application of the estimation and prediction methods described in this article.