Parameters Estimation of Three Mixed Exponential Distributions

Abstract

Mixed exponential distributions play an important role in life time data analysis, but if we use traditional statistical methods to estimate the parameters in the model, it will be very difficult, however we apply the generalized expectation maximization (GEM) algorithm, namely expectation conditional maximization (ECM) algorithm, to estimate the parameters of the model, it will greatly simplify the complexity of the calculation. In this paper, we study the parameter estimation problem in complete data situation, and give Monte Carlo (MC) simulation, which results show that the algorithm based on ECM to estimate the parameters of the mixed exponential distribution is very effective. Keywords-mixed exponential distribution; ECM algorithm; MC simulation I. INTRODUCTION In engineering, medicine, biology and etc, life time data analysis has became a problem which statisticians and actual workers are very concerned about. There are very good statistical methods about life data analysis for a single population, but in the practical life there often are more populations. Therefore, the study of the distribution of the mixed parameter estimation will become very important. Zhu Liping, Lu Yiqiang and Mao Shisong (1, 3) give estimation of parameters of the single parameter mixed exponential distribution with EM algorithm. Demester, Laird and Rubin (2, 4, 5) put forward the EM algorithm, which greatly simplifies the calculation of maximum likelihood estimation, is recently developed quickly and is widely used, and give out the generalized EM algorithm (namely GEM) when there is no explicit format in maximizing. For multidimensional parameters, Meng and Rubin (1, 6) give a special kind of GEM algorithm, which is called ECM algorithm, this algorithm retains the simplicity and stability of EM algorithm and greatly simplify the calculation in maximizing in EM algorithm. This paper gives estimation of parameter of mixed exponential distribution with the ECM algorithm in the complete data, and provides the MC simulation. Just considering the three mixed exponential distributions in the following. Set the subpopulation