Volume no :15, Issue no: 2, June (2016)

Journal of Statistics: Advances in Theory and Applications

GENERATIVE MECHANISMS OF A SURVIVAL TIME: THE CASE OF THE INVERSE WEIBULL MODEL

Author's: Pasquale Erto, Antonio Lepore and Biagio Palumbo
Pages: [113] - [130]
Received Date: June 17, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121675

Abstract

When only a small sample is available, it is well known that the empirical distribution contains scarce information about the shape of the hazard function as well as about the far-right tail of the “parent” probability density. So, the probabilistic analysis of the mechanisms that lead to the involved random variable can be a decisive factor to identify the appropriate distribution model. In this context, three recurrent degradation mechanisms (“simple degradation”, “stress-strength”, and “latent-defensive-attempts”) which lead exactly to the inverse Weibull survival time are identified and mathematically formulated. They are derived as first passage time distributions. Then, the proposed mechanism approach, applied to the proper identification of this relatively unknown survival model, is illustrated by means of two real world examples.

Keywords

disease modelling, damage accumulation, survival analysis, hazard rate, mean residual life.