论文标题
关于卡方变量加权总和的分布
On the Distribution of the Weighted Sum of Chi-Squared Variables
论文作者
论文摘要
本文介绍了中央独立卡方随机变量的加权总和，其概率分布函数（P.D.F.）和累积分布函数（C.D.F.），其基于使用力矩生成函数的方法，具有非零的重量。获得P.D.F.和C.D.F.在此功能中，我们首先使用部分分数分解或残基方法得出此加权总和的矩生成函数。结果涵盖了两个和三个加权卡方的随机变量的总和，可以很容易地适应更一般的情况。
This paper presents the probability distribution function (p.d.f.) and cumulative distribution function (c.d.f.) of the weighted sum of central independent chi-squared random variables with non-zero weighs based on a method using moment generating functions. To obtain the p.d.f. and c.d.f. of such a function, we first derive the moment generating function of this weighted sum using the partial fractions decomposition or the residue method. The results cover the sum of two and three weighted chi-squared random variables, which can easily be adapted to more general cases.
