A DISTRIBUTION-FREE METHOD USING MAXIMUM ENTROPY AND MOMENTS FOR ESTIMATING PROBABILITY CURVES OF ROCK VARIABLES

摘要

A distribution-free algorithm is presented in this paper, by combining maximum entropy with sample moments, for estimating probability curves directly from experimental or field sample data of rock random variables. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability curves. The sample moments may be conventional moments or probability-weighted moments (PWMs). Probability curves derived by maximum entropy and conventional moments are probability density functions (pdf), and probability curves derived by maximum entropy and PWMs are inverse cumulative density functions (ICDF). Example from test data of uniaxial compressive strength of a rock was presented for illustrative purposes. The results show that category of moments and sample size have significant influence on the estimation accuracy of probability curves of rock variable. The percentage relative error of estimation by PWMs is much smaller than that by conventional moments. Maximum entropy and PWMs enable more secure inferences to be made from small samples about an underlying probability curve, especially when the sample size is 40 or smaller.