Cross entropy quantile function estimation from censored samples using partial probability weighted moments

Extreme quantile estimation using the minimum entropy principle from complete or non-censored samples has been reported in the literature. However, censored samples are often encountered in many engineering analysis such as annual extremes of river discharge and stream flow analysis. In this paper, the principle of minimum cross entropy (CrossEnt) is extended to partial minimum CrossEnt principle, which is defined on a finite interval. By interpreting the partial probability weighted moments (PPWMs) as partial moments of quantile function, the paper presents a new distribution free method for estimating the quantile function of a non-negative random variable using the principle of partial minimum CrossEnt subject to constraints on PPWMs estimated from censored data. Numerical examples are performed to assess the accuracy of extreme quantile estimates computed from censored samples.