The Performance of Estimators for Generalization of Crack Distribution

Abstract

In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.