Statistical Inference For Lomax Distribution Based On Complete Data And Random Censored Data

Survival analysis is a method of analyzing survival time data,that is time-to-event data.It is involved in many application areas,such as medical clinical trials,reliability engineering,epidemiology,etc.In reliability theory,it is called life data or failure time data.The Lomax distribution was proposed by Lomax in 1954,and applied the Lomax distribution to economic failure data.Later,it has been applied in the fields of inequality,life and reliability modeling in income and wealth.This paper mainly discusses the parameter estimation problem of Lomax distribution under complete data and random censored data.The content of the article mainly includes the following parts.Firstly,under the complete data,the scale parameter of the Lomax distribution is known,when the loss function is the composite MLinex loss function,Bayesian estimation and E-Bayes estimation of shape parameters are discussed,and the related properties of E-Bayes estimation are proved,the numerical simulation shows that the estimation is effective.Then,under the random censored data,the expected test time,test observation time and maximum likelihood estimation of Lomax distribution parameters are studied.in the solution process,Newton-Raphson iterative method is used to approximate the estimated values of the parameters,finally maximum likelihood estimated,which have homomorphism,is obtained.Finally,under the random censored data,the Bayesian estimation problem of Lomax distribution is studied.when solving Bayesian estimation,it is found that it is more difficult to solve multiple integrals,the numerical solution is obtained by Lindley approximation and carried out numerical simulation.