Kumaraswamy Marshall-olkin Logistic Exponential Distribution:Properties And Application

With the development of science and technology and the progress of society,various products are constantly being introduced,and people's pursuit of product quality(lifetime)has continued to improve.Statistical models are applied in various fields,such as: finance,medical,engineering and biology.However,existing statistical models cannot fit all data,which requires constructing some efficient and widely used statistical models.In the inspection of product quality,many factors(such as manpower,time and money)are often considered to make a reasonable plan.It is difficult to obtain a complete sample.So censored samples are often selected for research.This article is mainly divided into three parts:In the first part,we propose a new five-parameter life distribution through the Kumaraswamy Marshall-Olkin extension method,called Kumaraswamy Marshall-Olkin logistic exponential distribution.It contains six distributions which are Kumaraswamy Marshall-Olkin exponential,Marshall-Olkin logistic exponential,Kumaraswamy exponential,Marshall-Olkin exponential,logistic exponential and exponential distributions.The hazard rate function of this distribution mainly has six shapes,namely: S,constant,increasing,decreasing,bathtub and inverted bathtub.So it can flexibly fit some more complex life data.The probability and statistical properties of the new distribution are studied,including quantile function,ordinary moment,incomplete moment,moment generating function,Bonferroni and Lorenz curves,entropy,mean deviation,random order and order statistics.In the second part,we study the parameter estimation problem of the new distribution based on the complete sample.First,we discussed six estimation methods for the new distribution,including maximum likelihood,ordinary least-squares,weighted least-squares,percentiles,Cram?er-von Mises and Bayes estimation methods.Then,the performances of the six estimation methods are compared using a Monte Carlo simulations study.Finally,under two real data sets(the hazard rate function shapes are increasing and bathtub type),the MLE and Bayes methods are used to estimatethe parameters,respectively.Comparing the data fitting results of the new distribution,its special case,the five-parameter Kumaraswamy Marshall-Olkin Weibull and the three-parameter Exponential-Weibull distribution,which illustrate the application value and application prospects of the new distribution.In the third part,we discuss the MLE and Bayes estimation of the new distribution parameters base on the generalized progressive type-II censoring scheme.The asymptotic confidence intervals of the parameters are obtained based on the observed Fisher's information matrix.The MCMC samples are obtained by the MetropolisHasting method,and then be used to compute the Bayes estimation under the mean square loss function as well as to construct the corresponding HPD credible intervals of the new distribution.Finally,the feasibility of the two estimation methods is illustrated based on numerical simulation and two real data sets.