Analysis of Waiting Time Using Three Mixtures Exponential Distribution

Abstract

Mixed exponential distributions play a significant role in lifetime data analysis, but if we use traditional statistical methods to estimate the parameters in the model, it will be very difficult. However, we employed the Expectation-Maximization (EM) algorithm to estimate the parameters of the model. It will simplify the complexity of the calculation. This paper studies the parameter estimation problem in a complete data situation and gives Monte Carlo (MC) simulation. The EM algorithm is good to estimate the parameters for the three mixed exponential distributions. The parameters estimating were remarkably close to the real values; simultaneously, the samples' RMSE values are more and smaller along with the increase of the sample size so that the method can be regarded as a kind of very effective statistical analysis calculation method. Results show that the algorithm based on EM to estimate the parameters of the mixed exponential distribution is remarkably effective. An application was made at the three phases waiting time in the Rasheed Bank in AL-Mustansiriyah University. The results showed that the estimating mean waiting time by EM algorithm for then the audit stage phase has the biggest proportional in this process which has formed (48%) from total mixture distribution component with scale parameter (0.46 hours), then the provide information phase (32%) with scale parameter (0.44 hours), then the stage of the cashier (20%) with mean waiting time (0.32 hours).