Resumen de Some insights on preservation of mixture age properties

Francisco Germán Badía Blasco , María Dolores Berrade Ursúa

• The hazard rate and the mean residual life are widespread measures of systems reliability.

  The reversed hazard rate and the mean inactivity emerge as dual functions that can be applied when dealing with left-censored data. It's well-known that lifetime distributions, usually positive, can not show increasing reversed hazard rates. Therefore we provide new characterizations for a random variable to be increasing hazard rate or decreasing reversed hazard rate. In addition we focus on age properties preservation under mixtures. Previous results show that both classes, the increasing reversed hazard rate and the decreasing mean inactivity time are preserved under mixtures. However these results can not be a applied when positive distributions are involved as in reliability studies. Hence we aim at obtaining mixture preserving conditions for decreasing reversed hazard rate distributions or increasing mean inactivity time distributions.