Estimators of contingent probabilities and means with actuarial applications

Contingent probabilities and means are ubiquitous in actuarial science. The correct interpretation of contingent probabilities and means as well as the probability theory behind them have been addressed by researchers. In this article, we explore their statistical aspect. We give non-parametric estimators of contingent probabilities and means. Then, we show that our estimators are strongly consistent. Moreover, we give the asymptotic distributions of our estimators. Finally, we provide several examples to demonstrate the applications of these estimators in actuarial science.