Statistical Inference Of Several Distributions Under Interval Censored Data And Empirical Analysis Of Financial Data

As a result of the objective conditions such as observation technology or experiment funds limit,we cannot get the exact value of the observation object in many practical statistical research problems.We only observed a range of value,and this kind of data is generally called censored data in statistical.Such as in medicine,when studying the law of disease outbreak time,we will get censored data.In engineering,when testing product lifetime,we will get censored data.In financial economics,when studying the duration of the trade relations,the bonds default time and enterprise life cycle,we will get censored data.There is a lot of censored data in medical,engineering,finance,economics,actuarial science and demography,so statistical analysis of censored data is very important.Current research of censored data mainly focused on relatively simple right censored data,and there are a few research results of interval censored data.The empirical analysis also focused in the field of medicine and engineering,more less in the field of financial economics and actuarial.In the paper,we study statistical inference of several survival distributions under interval censored data,using the idea of survival analysis of life data.Based on interval censored data,we estimate parameter of the exponential distribution,the Weibull distribution and the log-Logistic distribution.And we use three methods,which are the maximum likelihood estimation based on censored likelihood function,the EM algorithm and the ECM improving the M step of EM algorithm.Based on interval censored data,we simulate parameter estimation of three distribution using the above methods by Matlab software programming and R software,and we compare different interval censored samples under the three methods of estimation results.The simulation results show that,the above parameter estimation methods are feasible and effective.The ECM algorithm has good convergence properties and is superior to the EM algorithm in application.When the sample size is larger or the ratio of censored data is smaller,the effect of estimator is better.In addition,the confidence intervals have been obtained using asymptotic properties of variance-covariance matrix and we design the optimal censoring plan al using the principle of maximum of information,which are simulated by software.Finally,we investigate the real interval censored time data in the field of financial economics,which is the duration of export from China to America during2004-2014,and we find that the estimation of Weibull survival function is consistentwith the theory of survival function.All the results in this paper show that the proposed methods are of better significance in both theory and practice.