Some improvements on generalized reversed aging intensity functions

Ricerche di Matematica, vol. 74, pp. 819–834

Abstract

Abstract Recently, the generalized reversed aging intensity functions have been studied in the literature revealing to be a tool to characterize distributions, under suitable conditions. In this paper, some improvements on these functions are given and the relation between two cumulative distribution functions leading to the same generalization is studied. In particular, a link with the two-parameters Weibull distributions is found and a new stochastic order is defined in terms of the generalized reversed aging intensity. This order is strictly related to the definition of extropy, that is the dual measure of entropy, and some connections with well-known stochastic orders are analyzed. Finally, the possibility of introducing the concept of generalized aging intensity is studied also in terms of cumulative distribution functions with non-positive support.

Authors 3

1. Francesco Buono corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Maria Longobardi

   University of Naples Federico II

   Affiliation as printed

   Università di Napoli Federico II, Naples, Italy

3. Magdalena Szymkowiak

   Poznań University of Technology

   Affiliation as printed

   Poznan University of Technology, Poznan, Poland