A Generalization of the Half-Normal Distribution with Applications to Lifetime Data

Abstract

A two-parameter family of lifetime distribution which is derived from a model for static fatigue is presented. This derivation follows from considerations of the relationship between static fatigue crack extension and the failure time of a certain specimen. The cumulative distribution function (cdf) of this new family is quite similar to the cdf of the half-normal distribution, and therefore this density is referred to as the generalized half-normal distribution (GHN). Furthermore, this GHN family is a special case of the three-parameter generalized gamma distribution. Even though the GHN distribution is a two-parameter distribution, the hazard rate function can form variety of shapes such as monotonically increasing, monotonically decreasing, and bathtub shapes. Some properties of this family are given, and examples are cited to compare with other commonly used failure time distributions such as Weibull, gamma, lognormal, and Birnbaum-Saunders.