Parameter Estimation of the Shape Parameter of the Castillo–Hadi Model

Abstract

In Castillo and Hadi [Castillo, E., Hadi, A. S. (1995). Modeling lifetime data with application to fatigue models. J. Amer. Statist. Assoc. 90:1041–1054], a new model for the analysis of lifetime data in the presence of a covariate is presented. The model is derived based on physical and statistical considerations. In this article, we focus on estimation of the power parameter of this model, and propose the new methods for estimation based on the location-scale-free transformation.

Key Words:

• Fatigue model
• Power parameters
• Transformation free from location and scale parameter
• Mixture distribution
• Method of moments

Acknowledgment

The authors are grateful to the anonymous referees and the associate editor for their helpful comments.