ESTIMATION OF PARAMETERS OF GENERALIZED BETA OF THE SECOND KIND (GB2) DISTRIBUTION BY MAXIMUM LIKELIHOOD ESTIMATION (MLE) AND NEWTON-RAPHSON ITERATION

The aim of this study is to derive the estimates of the parameters of generalized beta of the second kind (GB2 ) distribution by using the maximum likelihood estimation (MLE ). Due to the difficulty in finding the analytical solution by MLE approach, the estimate is determined numerically by using iteration and Newton-Raphson methods. The Newton-Raphson method is used to estimate parameters, to find a confidence interval, to estimate the bias, and to estimate the variance for some difference sample size configuration viz. for n =30,50,100,20nand 500. The estimation of the parametersa, b, p and q attains the values close to the real value of theparameters. If the size of the sample increases, the confidence intervalbecomes narrower and the bias and variance become smaller.