Some Properties of the Three-Parameter Crack Distribution

Abstract

The purpose of this paper is to investigate the main theoretical properties of a new lifetime three-parameter family of distributions. We will call this family as Crack distribution (CR) because it may be applied for modeling of some physical characteristics of fatigue cracks. CR-distribution relates to the following two-parameter distributions : the Birnbaum-Saunders distribution, the Inverse Gaussian distribution and the Length Biased Inverse Gaussian distribution. These are well-known fatigue-lifetime distributions. They are the special cases of CR-distribution based on non-classical parametrization. The main theoretical properties such as the characteristic function, the moment generating function and the cumulative distribution function on three-parameter CRdistribution are established in closed form.