An Additive Perks–Weibull Model with Bathtub-Shaped Hazard Rate Function

Abstract

In this article, an additive Perks–Weibull model capable of modeling lifetime data with bathtub-shaped hazard rate function is proposed. The model is derived by the sum of the hazard rates of Perks and Weibull distributions. Some statistical properties including shapes of density and hazard rate functions, moments, and order statistics are explored. The method of maximum likelihood estimation is used for estimating the model parameters. The goodness-of-fit of the model for three real datasets having bathtub-shaped hazard rate functions has been illustrated. Finally, an application for competing risk data is also given to show the flexibility of the proposed model.

Keywords

Perks distribution / Weibull distribution / Additive model / Bathtub hazard rate function / Maximum likelihood estimation / Competing risk analysis