Estimation of minimum cross-entropy quantile function using fractional probability weighted moments

The principle of minimum cross-entropy provides a systematic approach to derive the posterior distribution of a random variable given a prior and additional information in terms of its product moments. This approach can be extended to derive directly the quantile function by using probability weighted moments (PWMs) as constraints in the cross-entropy minimization approach, as shown in a previous study [Pandey MD. Extreme quantile estimation using order statistics with minimum cross-entropy principle. Probabilistic Engineering Mechanics 2001;16(1):31–42]. The objective of the present paper is to extend and improve the previous method by incorporating the use of the fractional probability weighted moments (FPWMs) in the place of conventional integer-order PWMs. A new and general estimation method is proposed in which the Monte Carlo simulations and optimization algorithms are combined to estimate FPWMs that would subsequently lead to the best-fit quantile function. The numerical examples presented in the paper show a substantial improvement in accuracy by the use of the proposed method over the conventional approach.