Estimating Parameters for Extension of Burr Type X Distribution by Using Conjugate Gradient in Unconstrained Optimization

The conjugate gradient method used to estimate the parameter of marshall-olkin exponentiated burr type x distribution (moebx). the proposed distribution moebx based on the work by (marshall–olkin 1997). several properties of the moebx distribution were investigated and studied such as quantile function, moments, moment generation function and order statistics. the estimation process by maximum likelihood estimation maybe an obstacle for statisticians, so used conjugate gradient method in unconstrained optimization to estimate parameters. it was employed for estimating the three parameters of the new distribution. the flexibility of the moebx was illustrated by using two real data sets. we compared with nested and no nested distributions and encouraging results were obtained using a real data set.