Statistical Inference And Analysis Of Inverse Exponentiated Rayleigh Distribution Based On Different Progressively Censored Competing Risks

In the lifetime test,censoring scheme makes the experiment process faster and saves the cost to a great extent.The research and exploration of product failure causes make the model more in line with the actual situation.The previous progressive censoring of single failure cause has been unable to meet the actual needs.The hazard function of Inverted Exponentiated Rayleigh distribution has the nonmonotonicity,which can well match the product failure trend in real life.This paper mainly studies the statistical inference and analysis of the Inverted Exponentiated Rayleigh distribution based on type-II progressively censored competing risks data and type-Ⅰ progressively hybrid censoring with dependent competing risks.First,the type-Ⅱ progressively censored competing risks model of Inverted Exponentiated Rayleigh distribution is studied.The existence and uniqueness of maximum likelihood estimators for parameters are proved and the corresponding forms are also given.The estimates are obtained by Newton-Raphson iterative method.Through the Fisher information matrix and the asymptotic normality of the maximum likelihood estimators,the asymptotic confidence intervals are given.Further,bootstrap method is proposed for small sample size,and bootstrap confidence interval is calculated.Importance sampling method is used to obtain Bayesian estimates and the highest posterior density credible intervals under square error loss function and Linex loss function.Then,the Monte Carlo simulation study makes a detailed explanation and comparison of the above methods.A real data set example is applied to show the practical use.Finally,a summary is proposed.Second,the causes of product failure are often not independent of each other in real life.The failure of the product can be caused by one of the reasons,or can be caused by a variety of reasons.Therefore,this paper also studies the statistical inference problem of dependent competing risks data under type-I progressively hybrid censoring.The joint survival function and joint density of dependent failure causes are constructed.On the basis,maximum likelihood estimates of parameters are given,and the approximate confidence intervals are obtained by asymptotic likelihood theory.Metropolis-Hastings algorithm and Gibbs sampling method are used to obtain the point estimates and the highest posterior density credible intervals of bayes estimation.Monte Carlo simulation and data analysis are taken for verification and interpretation,and a summary of the model is proposed.At the end,all the models and results that have obtained are summarized.