Derivation of sample oriented quantile function using maximum entropy and self‐determined probability weighted moments: Fid-Bau Portal

Derivation of sample oriented quantile function using maximum entropy and self‐determined probability weighted moments

Deng, Jian / Pandey, M. D.

10.1002/env.955.abs

The paper proposes a new distribution free method for deriving the quantile function of a non‐negative random variable using the principle of maximum entropy (MaxEnt) subject to constraints in terms of the self‐determined probability‐weighted moments estimated from observed sample data. The principle of MaxEnt constrained by probability weighted moments (PWMs) was utilized to estimate the quantile function. For correct estimation of a quantile function, outliers must be rationally considered in the analysis. However, conventional PWM was criticized for assigning non‐exceedance probabilities to sample points based on only their rank number in an ordered series rather than the magnitude of the points themselves, hereby being unable to satisfactorily accommodate outlier in a finite sample. The difficulty in obtaining accurate PWM estimates from samples has been the main impediment to the application of the MaxEnt Principle in extreme quantile estimation. This paper is an attempt to circumvent this difficulty by the use of self‐determined probability‐weighted moments, which are completely decided by the distribution itself and sample data's magnitude. By interpreting the SD‐PWM as moment of quantile function, the paper derives a more rigorous quantile function using MaxEnt principle, which is extraordinarily suitable for cases with small samples containing outliers. An efficient algorithm is presented to estimate the unknown parameters of this sample oriented MaxEnt QF. Comparative studies and numerical analysis are performed to assess the accuracy of the proposed QF estimation method. Copyright © 2009 John Wiley & Sons, Ltd.