In this article, We consider the estimation problems of the parameter and reliability function of the generalized Pareto distribution based on a progressively type-II censored sample with random (Binomial) removals. we use the method of maximum likelihood and Bayesian estimation to estimate parameter and reliability function. Bayesian estimates are derived under squared error and LINEX loss functions. we also construct the confidence interval for the parameter of generalized Pareto distribution based on a progressively type-II censored sample with random removals. The comparisons between different estimators are made based on simulation study.

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This paper considers Bayesian estimation of parameter and reliability function of Kumaraswamy-inverse Rayleigh distribution under the different loss functions with progressively first failure censored samples. We used squared error , minimum expected, weighted and Linex loss functions for obtaining the Bayes estimators of parameter and reliability function. Finally, Comparisons are made between Bayes estimators under different loss functions using simulation study.