混合卡方随机变量和的近似分布的一个注记

APPROXIMATIONS TO DISTRIBUTION OF THE SUMMATION OF CHI-SQUARED VARIABLES

用形如b_1χ_(m_1)~2+b_2χ_(m_2)~2+c的随机变量的分布来近似混合卡方随机变量和的分布.采用前五阶累积量来确定分布函数的参数,给出了基于密度函数的误差上界并且证明该方法比文献中所用的形如ξχ_d^2+η的近似方法更能有效地控制犯第一类错误的概率.

In this article,we attempt to approximate the Chi-squared-type mixtures by a random variable with the distribution of form b1χm1^2＋b2χm2^2＋c,where the parameters are determined by the first five cumulants of the Chi-squared-type mixtures.We give the error bounds based on the density function and prove that the approximation has a better control of type I error rates than the commonly used ξxd^2 ＋ ηapproximation.