Estimation of the maximum entropy quantile function using fractional probability weighted moments

In a previous study, the conventional or integral-order probability weighted moments (IPWM) and the principle of maximum entropy were combined to derive an analytical form of the quantile function of a random variable [Pandey MD. Direct estimation of quantile functions using the maximum entropy principle. Struct Safety 2000;22(1):61–79]. This method is extended and improved in the present paper by utilizing the concept of fractional probability weighted moments (FPWMs). A general estimation method is proposed in which the Monte Carlo simulations and optimization algorithms are combined to estimate fractionals of FPWM that would lead to the best-fit quantile function. The numerical examples presented in the paper illustrate that the accuracy of the proposed FPWM based quantile function is superior to that estimated from the use of conventional IPWMs.