Abstract
In this article, the problem of estimating unknown parameters of the inverted kumaraswamy (IKum) distribution is considered based on general progressive Type-II censored Data. The maximum likelihood (MLE) estimators of the parameters are obtained while the Bayesian estimates are obtained using the squared error loss(SEL) as symmetric loss function. Also we used asymmetric loss functions as the linear-exponential loss (LINEX), generalized entropy (GE) and Al-Bayyati loss function (AL-Bayyati). Lindely's approximation method is used to evaluate the Bayes estimates. We also derived an approximate confidence interval for the parameters of the inverted Kumaraswamy distribution. Two-sample Bayesian prediction intervals are constructed with an illustrative example. Finally, simulation study concerning different sample sizes and different censoring schemes were reported.
Highlights
In most of life-testing experiments, the censored samples used when the experimenter wants to terminate the experiment early before all units are failed due to the time limitation and the huge cost of the experiment.Type-I and Type-II are the two basic types of censoring schemes, where in Type-I the experiment is terminated at pre-specified time point and the number of failures is variable, while the experiment under Type-II is terminated after a fixed number of failures
Concluding remarks In this work, we study the estimates for the parameters of inverted Kumaraswamy distribution under the general progressive censored samples
Two sample Bayesian prediction intervals are conducted for a future sample depending on the old sample units
Summary
In most of life-testing experiments, the censored samples used when the experimenter wants to terminate the experiment early before all units are failed due to the time limitation and the huge cost of the experiment.Type-I and Type-II are the two basic types of censoring schemes, where in Type-I the experiment is terminated at pre-specified time point and the number of failures is variable, while the experiment under Type-II is terminated after a fixed number of failures. Many authors have been studied the general progressive censoring using different lifetime distributions, as, Soliman (2008) make an inference for Pareto model using general progressive censored data. The Bayesian prediction was discussed by many authors based on different distributions with different types of censored samples as Mohie El-Din and Shafay (2013), they study Bayesian prediction intervals based on progressively Type-II censored data. Shafay and Balakrishnan (2012) study the Bayesian prediction intervals based on the Type-I hybrid censored data. Bayesian prediction intervals of generalized order statistics based on multiply Type-II censored data was discussed by Mohie El-Din et al(2012), they studied the Bayesian prediction for order statistics from a general class of distributions based on left Type-II censored data, see (2011). Latest Mohie El-Din et al (2017) study the One-sample Bayesian prediction intervals based on Type-II progressively hybrid censored samples. The maximum likelihood estimators for the reliability function R(x) and the hazard function h(x) , denoted by R(x)ML and h(x)ML can be obtained from (3) and (4) by replacing and by ˆML and ˆML , respectively
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