论文标题
非中心分布的混合表示
Mixture representations of noncentral distributions
论文作者
论文摘要
在实际线路上的任何对称分布$μ$中，我们可以将非中性分布的参数族与$（x+δ）^2 $，$δ\ not = 0 $的分布相关联，其中$ x $是一个随机变量，带有分布$μ$。 如果$μ$是标准正态分布，则会出现经典案例，导致非中央卡方分布。众所周知，这些可能被写成具有奇特自由度的中央卡方分布的泊松混合物。我们获得了逻辑分布和双曲线分布分布的这种混合物表示。我们还得出了卡方分布的替代表示，并将其与泊松家族的代表联系起来。 尽管这些问题源于参数统计数据，但它们也出现在广义的第二射线骑士定理的上下文中，该定理连接了高斯过程和马尔可夫过程的当地时代。
With any symmetric distribution $μ$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+δ)^2$, $δ\not=0$, where $X$ is a random variable with distribution $μ$. The classical case arises if $μ$ is the standard normal distribution, leading to the noncentral chi-squared distributions. It is well-known that these may be written as Poisson mixtures of the central chi-squared distributions with odd degrees of freedom. We obtain such mixture representations for the logistic distribution and for the hyperbolic secant distribution. We also derive alternative representations for chi-squared distributions and relate these to representations of the Poisson family. While such questions originated in parametric statistics they also appear in the context of the generalized second Ray-Knight theorem, which connects Gaussian processes and local times of Markov processes.
