论文标题
密度函数的两侧不等式的卡方变量的最大加权总和
Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
论文作者
论文摘要
构建了两侧边界，以达到卡方变量加权总和的概率密度函数。考虑了中央和非中心卡方变量的病例。上限和下限对总和的参数具有相同的依赖性，并且仅在绝对常数方面有所不同。在比较希尔伯特空间中的两个高斯随机元件和多维中心极限定理（包括无限维情况）中，获得的估计值将是有用的。
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence on the parameters of the sum and differ only in absolute constants. The estimates obtained will be useful, in particular, when comparing two Gaussian random elements in a Hilbert space and in multidimensional central limit theorems, including the infinite-dimensional case.
