Some remarks on the hazard functions of the inverted distributions

Abstract

The probability models of reciprocals of normal, Gamma and Weibull variates are called inverted normal, inverted Gamma and inverted Weibull distributions respectively. These distributions arise naturally in the study of certain stochastic processes causing wear-out failures of mechanical systems.^1–4 In this paper characteristic features of the hazard functions based on this inverted class of distributions are discussed and their possible uses are explored. Hazard functions and mean residual life of inverted normal, inverted Gamma and inverted Weibull are compared with the normal, Gamma and Weibull hazards.