关于部分非中心卡方分布函数矩的计算

Approximating the mode of the non-central chi-squared distribution

In this paper we consider the probability density function (PDF) of the non-central $χ^2$ distribution with arbitrary number of degrees of freedom and non-centrality. For this function we find the approximate location of the maximum and discuss related edge cases of 1 and 2 degrees of freedom. We also use this expression to demonstrate the improved performance of the C++ Boost's implementation of the non-central $χ^2$ and extend the domain of its applicability.

Squared chaotic random variables: new moment inequalities with applications

We prove a new family of inequalities involving squares of random variables belonging to the Wiener chaos associated with a given Gaussian field. Our result provides a substantial generalisation, as well as a new analytical proof, of an estimate by Frenkel (2007), and also constitute a natural real counterpart to an inequality established by Arias-de-Reyna (1998) in the framework of complex Gaussian vectors. We further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials, thus partially improving results by Pinasco (2012), as well as to obtain a novel proba…

广义F分布的计算

Computation of the Generalized F Distribution

精确的表达式给出的分布函数的比例的一个独立的卡方变量的加权和一个单一的卡方变量，适当缩放。该分布是经典F分布对卡方变量混合的推广。该分布是根据劳里塞拉函数。给出了用超几何函数表示的截断误差界。给出了联合异常值和Hotelling误定T^2分布的检测应用。