The distribution of the residual lifetime and its applications

Abstract

Let T be a continuous positive random variable representing the lifetime of an entitle This entity could be a human being, an animal or a plant, or a component of a mechanical or electrical system. For nonliving objects the lifetime is defined as the total amount of time for which the entitj'^ carries out its function satisfactoriljc The concept of aging involves the adverse effects of age such as increased probability of failure due to wear. In this thesis, we consider certain characteristics of the residual lifetime distribution at age t, such as the mean, median, and variance, as descril)ing aging. The following families of statistical distributions are studied from this point of view: 1. Gamma with two parameters, 2. Weil^ull with two paxameters, .3. Lognormal with two parameters, 4. Inverse Poljmomial with one parameter. Gamma and Weil)ull distrilDutions are fitted to actual data.