A comparison between modified maximum likelihood and maximum likelihood methods for a three-parameter gamma distribution

Abstract

In this research, empirical  data were generated through the cumulative  function of the three-parameter gamma distribution by Monte Carlo method for five different sample sizes (25, 50, 75, 100, 150), and for different values ​​of parameters at each sample size, and estimation of the parameters of the gamma distribution of the empirical  data in two methods is the  maximum likelihood method and the modified maximum likelihood  method. The preference of the modified maximum likelihood  method was best  through the use of the statistical criterian  mean square error MSE and the statistical criterian absolute  mean square error MAPE