Modeling failure time data by lehman alternatives

TLDR

The proportional hazards model is widely used to model failure time data. The paper proposes a new model for failure time data defined by F*(t) = [F(t)]^θ, where F(t) is the baseline distribution and θ > 0. The authors analyze the monotonicity of the resulting failure rates and investigate order relations among them. The model can generate both monotonic and non‑monotonic failure rates, and the authors illustrate this with exponentiated Weibull, exponential, gamma, and Pareto examples.

Abstract

The proportional hazards model has been extensively used in the literature to model failure time data. In this paper we propose to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number. This model gives rise to monotonic as well as non-monotonic failure rates even though the baseline failure rate is monotonic. The monotonicity of the failure rates are studied, in general, and some order relations are examined. Some examples including exponentiated Weibull, exponential, gamma and Pareto distributions are investigated in detail.