Some properties of conditional partial moments in the context of stochastic modelling

There are many practical situations where the access to conditional distributions are more likely than to their joint distribution. In the present paper we study partial moments in the conditional setup. It is shown that the conditional partial moments determine the corresponding distribution uniquely. The relationships with reliability measures such as conditional hazard rate and mean residual life are obtained. Characterizations results based on conditional partial moments for some well known bivariate lifetime distributions are derived. We study properties of conditional partial moments in the context of weighted models. Characterizations of conditional partial moments using income gap ratio are also obtained. Finally, non parametric estimators for conditional partial moments are introduced which are validated using simulated and real data sets.

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