Characterizations from Relationships Between Failure Rate Functions and Conditional Moments

摘要

We obtain general results on characterization of distributions from relationships between failure rate functions and conditional moments. Specifically, we study characterizations from linear relationships between the usual failure rate function and the left truncated conditional moment m_h(x) = E(h(X) | X > x), extending some characterizations of mixtures given recently. Moreover, we also study characterizations from relationships between the generalized failure rate functions and the doubly truncated conditional moment function m_h(x,y) = E(h(X) | x < X < y). Our results extend some particular characterizations based on mean residual life and failure rate. As a consequence, we obtain characterizations based on reversed failure rate and reversed mean residual life (expected inactivity time). Finally, we apply our theoretical results to obtain some new characterizations for usual models.