Parameter Estimation Of Three-parameter Pareto Distribution With Interval Censored Data

In survival analysis,due to objective conditions,it is sometimes impossible to know the specific time of the events,only the time interval of the events can be known,which leads to interval censored data.Given the distribution form of population,estimating the population distribution based on interval censored data has always been a research hotspot.However,at present,there is no special research on parameter estimation of interval censored data which is subject to three-parameter Pareto distribution.This paper mainly studies the parameter estimation of three-parameter Pareto distribution with interval censored data.In this paper,the maximum likelihood estimation method uses the likelihood function based on censored data.Combined with probability weight moment method and Newton-Raphson method,the maximum likelihood estimation method is proved to be consistent and asymptotically normal.In addition,the Bayesian method based on MCMC method is discussed under the three priors of uniform prior,Jeffreys prior,Gamma prior and the three losses of square loss,Linex loss,entropy loss.Finally,this paper tests the feasibility of these methods through simulation and demonstration.The simulation results are good.With the increase of sample size and observation times,the root mean square error of the estimates obtained by the two methods will decrease.In addition,this paper compares the performance of the two methods under different sample sizes,and the root mean square error of Bayesian estimation under different priors and loss functions,so as to provide a reference for choosing estimation methods when processing data in reality.