The Inverse Weibull Survival Distribution and its Proper Application

TL;DR

This paper explores the properties and applications of the Inverse Weibull distribution, demonstrating its unique upside-down bathtub hazard shape, proposing mechanisms leading to it, and developing methods to distinguish it from similar models.

Contribution

It introduces three generative mechanisms for the IW distribution, and proposes a discriminating procedure using statistical criteria to identify it among UBT models.

Findings

IW distribution has upside-down bathtub hazard function.

The proposed discriminating criteria are invariant and effective.

Monte Carlo simulations show high probability of correct model selection.

Abstract

The peculiar properties of the Inverse Weibull (IW) distribution are shown. It is proven that the IW distribution is one of the few models having upside- down bathtub (UBT) shaped hazard function. Three real and typical de generative mechanisms, which lead exactly to the IW random variable, are formulated. So a new approach to proper application of this relatively unknown survival model is supported. However, we consider also the case in which any knowledge about generative mechanism is unavailable. In this hypothesis, we study a procedure based on the Anderson-Darling statistic and log-likelihood function to discriminate between the IW model and others alternative UBT distributions. The invariant properties of the proposed discriminating criteria have been proven. Based on Monte Carlo simulations, the probability of the correct selection has been computed. A real applicative example closes the paper.