Extreme quantile estimation from censored sample using partial cross-entropy and fractional partial probability weighted moments

Quantile function (QF) estimation by using minimum cross-entropy principle from complete or non-censored samples was reported before [Pandey MD. Extreme quantile estimation using order statistics with minimum cross-entropy principle. Probabilist Eng Mech 2001;16(1):31–42]. However, censored samples are often encountered in engineering reliability and hydrology distribution analysis. This paper presents a new distribution free method for estimating the quantile function of a non-negative random variable using the principle of partial minimum cross-entropy subject to constraints specified in terms of fractional partial probability weighted moments (FPPWMs) estimated from censored observed data. The proposed method exhibits considerable flexibility and covers two special cases. The numerical results show that substantial improvement in efficiency and accuracy of quantile estimation by use of the new method over other approaches.