关于可靠性工程中拟合概率密度的注记

本文从Sturm-Liouville方程的本征函数构成的加权正交多项式系的观点对工程上常用的用正态、Gamma、Beta密度拟合概率密度f(x)^3,4]作统一解释.结果表明,用第一、二阶矩决定上述双参数密度的两个参数时,恰好使f(x)的关于相应的加权正交多项式系作展开时前两个广义Fourier系数为0.

NOTES ON FITTING PROBABILITY DENSITY FUNCTIONS IN RELIABILITY ENGINEERING

In engineering the density functions of normal, gamma and beta distributions are often used to fit other pdf f(x). The way to do it is to determine the two parameters in those distributions mentioned above by the first two moments. From the fact that the eigenfunctions of Sturm-Liouville equation form complete orthogonal series, it is shown here that the method usually used just makes the first two generalized Fourier coefficients of the orthogonal expansion of f(x) with respect to the orthogonal series equal to zero.