Statistical Inference And Empirical Study Of Inverted Exponentiated Rayleigh Distribution Based On Censored Samples

In this paper,we study statistical inference and empirical study of the inverted ex-ponentiated Rayleigh distribution under progressive type ? censored sample and pro-gressively first-failure censoring sample.The samples considered is able to greatly save the cost of the experiment and speed up the experiment.Specifically,the pivotal in-ference is proposed to estimate the two unknown parameters of the inverse exponential Rayleigh distribution based on progressive type ? censored data.We derive the point estimator and construct an interval estimator using pivotal quantity method.To com-pare the performance of this proposed method and the traditional maximum likelihood estimation method,a simulation study is conducted.The simulation results show that the proposed method performs better in terms of biases and MSEs.And more,we investigate the lifetime performance index based on the inverted exponential Rayleigh distribution using progressive type ? censored samples.life-time performance index is a powerful and efficient way to analyze whether a product achieves the specified standards.We derive the estimation value of lifetime performance index with the help of maximum likelihood method,meanwhile conduct the hypothesis test.Based on extensive simulation,power function is utilized to assess effectiveness of hypothesis testing.The simulation results show that lifetime performance index is good for determining whether the lifetime of the product reaches the criterion.Progressively first-failure censoring sample is a more complicated sampling method than progressive type ? censored sample.We deal with Maximum likelihood and Bayes estimators of inverse exponential Rayleigh distribution with progressively first-failure censored data.The observed Fisher matrix is conducive to obtain asymptotic confidence interval.Parametric bootstrap methods are applied to provide the confidence intervals.Bayes estimators in terms of squared error loss function are derived with Metropolis-Hastings technique,which are helpful to construct highest posterior density credible intervals.We compare the behavior of various estimators by conducting Monte Carlo simulations.