Residual life functionals at great age

Abstract

The mean residual life (MRL) function is the mean of the conditional distribution P(X - t ϵ |X> t) as a function in t. First, it will be shown that the empirical MRL function is an inaccurate estimator of the Pareto MRL function if the shape parameter is close to 1. Therefore, other parameters of this conditional distribution such as the median and certain trimmed means are investigated. The median and the trimmed mean residual life functions possess again the property of being linear in t and can therefore be used for a visual model selection. We will prove the asymptotic normality of these statistics at increasing ages t within the framework of residual life functionals.

Keywords:

• residual life functionals
• trimmed mean residual life function
• median residual life function
• survival function
• pareto distribution
• rate of convergence
• asymptotic normality