Estimating probability curves of rock variables using orthogonal polynomials and sample moments

来源期刊：中南大学学报(英文版)2005年第3期

论文作者：邓建 边利

文章页码：349 - 353

Key words：rock variables; probability curve; orthogonal polynomials; conventional moments; probability-weigh-ted moments

Abstract: A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.