On a generalization of crack distribution

The Crack distribution is a lifetime distribution which is useful for statistical analysis in Physics and Engineering problems. A lifetime distribution provides the information that motivates practitioners to protect against damages after the lifetime of machine element or something terminated by the fatigue crack phenomena. The three-parameter distribution is a mixture of the two-parameter of Inverse Gaussian distribution and Length Biased Inverse Gaussian distribution.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 q where >0,>0,0≤p≤1,0≤q≤1 and p+q≤1. We investigate the properties of Generalized Crack distribution including the first four moments, the mean and variance, the characteristic function. We estimate the four-parameter by using the method of moment estimation, the maximum likelihood estimation and EM-algorithm method. Evaluate the performance of the estimators by using bias and mean square error via simulation study based on MCMC. In addition, the two real data sets were analyzed. The results of simulation are presented in numerically and graphically.