Statistical Inference Of Pareto Distribution Based On Complex Censored Data

The Pareto distribution has a wide range of applications and plays an important role in describing the urban population,stock prices,and income distribution.Compared with complete data,the censored data has the advantage of saving time and expenses.This paper studies the statistical characteristics of the Pareto distribution based on a variety of complex censored data,constructs a goodness-of-fit test under progressive type II censoring,then derives the statistical inference for the lifetime performance index of the Pareto distribution based on the general progressive type II censored data.This article discusses the analysis of the competitive risk model of the Pareto distribution with the adaptive progressively type II censored scheme,and extends the conclusions to the generalized exponential distributions which are more complex.First,we develop a goodness-of-fit test process for Pareto distribution based on progressive type II right censoring data.Based on data transformation and the nonparametric estimation of the hazard function,a goodness-of-fit test statistic is constructed.The empirical distribution of the test statistics is obtained.The distribution of the test statistics is independent of the selection of the parameters but related to the censoring percentage.Afterwards,Monte Carlo simulation is performed to evaluate the performance of the test statistics proposed in this paper,and the process of goodness-of-fit test is demonstrated through the analysis of real data.Then we study the statistical inference for the lifetime performance index of the Pareto distribution based on the general progressive type II censored data.Through data transformation,we derive the maximum likelihood estimator of lifetime performance index and confidence interval.Further,the Bayesian estimator and the associated credible interval based on informative and non-informative prior functions are also considered under the squared error loss function.Based on the non-Bayesian and Bayesian estimators of lifetime performance index,the hypothesis testing process is constructed to evaluate the life performance of products.After the Monte Carlo simulation,we find that the Bayesian estimator is far better than maximum likelihood estimator by comparing the mean square errors,and the Bayesian estimator based on informative prior has the best performance among the proposed estimators.The estimated mean squared errors for both maximum likelihood estimator and Bayesian estimator are small,indicating that our considered method is effective to assess the lifetime performance of the products,and a numerical example is analyzed for illustrative purposes.Finally,the competitive risk model of Pareto distribution with the adaptive progressively type II censored scheme is studied in this paper and the corresponding results are extended to a more complex generalized exponential distribution.Maximum likelihood estimator and approximate confidence intervals for unknown parameters are constructed by the Delta method.The Markov chain Monte Carlo(MCMC)method is utilized to obtain Bayesian estimates and credible intervals based on both the informative priors and non-informative priors.Furthermore,Monte Carlo simulations are performed to evaluate the performance of the proposed estimators.Finally,a numerical example is analyzed to illustrate the proposed inference methods.