A Generalized Family of Lifetime Distributions and Survival Models

Abstract

In lifetime data, the hazard function is a common technique for describing the characteristics of lifetime distribution. Monotone increasing or decreasing, and unimodal are relatively simple hazard function shapes, which can be modeled by many parametric lifetime distributions. However, fewer distributions are capable of modeling diverse and more complicated shapes such as N-shaped, reflected N-shaped, W-shaped, and M-shaped hazard rate functions. A generalized family of lifetime distributions, the uniform-R{generalized lambda} (U-R{GL}) are introduced and the corresponding survival models are derived, and applied to two lifetime data sets. The survival model is applied to a right censored lifetime data set.