两参数β分布卷积的数值计算

Numerical Calculations of Convolution of Double-Parameter Beta Distribution

本文从应用角度出发,对两参数β分布的卷积——独立随机变量之和的分布密度函数进行了控讨。通过对β分布的二重、三重、四重卷积的推导,得出了一些普遍规律,从而推出了计算两参数β分布的n重卷积的表达式。

A series of approximate calculation based on the ground of practical application have been given for convolution of double-parameter Beta distribution i. ex. the distribution function of the summation of the independent Beta distribution random variable (using the first three terms of e^x expansion formula and omitting the terms above x^3 ). Some regular patterns and there by an expression for calculating n-convolution of Beta distribution are derived from double, triple, and quadruplex convolution.