The Weibull–Pareto Composite Family with Applications to the Analysis of Unimodal Failure Rate Data

Abstract

The Weibull distribution is composited with Pareto model to obtain a flexible, reliable long-tailed parametric distribution for modeling unimodal failure rate data. The hazard function of the composite family accommodates decreasing and unimodal failure rates, which are separated by the boundary line of the space of shape parameter, gamma, when it equals to a known constant. The least square and maximum likelihood parameter estimation techniques are discussed. The advantages of using the proposed family are demonstrated and compared by illustrating well-known examples: guinea pigs survival time data, head and neck cancer data, and nasopharynx cancer survival data.

Keywords:

• Kaplan–Meier curve
• Pareto
• Right censoring
• Unimodal failure rate
• Weibull

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62N02, 62P10

Acknowledgment

A referee and the Editor were very helpful in revising an earlier version.