A new method for selection of population distribution and parameter estimation

An optimization method for parameter estimation is presented with the Kolmogorov-Smirnov distance used as the objective. A step-by-step implementation procedure is given. The method is demonstrated by estimating the parameters for three-parameter Weibull distributions from three different samples (with different sample sizes). A comparison of the proposed method and the usual methods such as the least-squares method, the matching moments method and the maximum likelihood method shows that more reasonable estimates of the parameters are given by the proposed optimization method. Then, the proposed method is successfully extended to estimate the parameters for the sum of two three-parameter Weibull distributions. Based on these findings, a new procedure for selection of population distribution and parameter estimation is presented.