Stochastic representations of star-shaped distributed random vectors having heavy or light tail density generating function g are studied for increasing dimensions along with corresponding geometric measure representations. Intervals are considered where star radius variables take values with high probability, and the derivation of values of distribution functions of g-robust statistics is proved to be based upon considering random events whose probability is asymptotically negligible if the dimension of the sample vector is approaching infinity. Moreover, a principal component representation of p-generalized elliptically contoured p-generalized Gaussian distributions is discussed.

中文翻译：

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高维星形分布

为了增加尺寸，研究了具有重或轻尾密度生成函数g的星形分布随机矢量的随机表示以及相应的几何度量表示。考虑星际半径变量具有高概率值的时间间隔，并且证明了g稳健统计量的分布函数的值的推导是基于考虑随机事件的，如果样本矢量的维数趋于无穷大，则概率的渐近可忽略。此外，讨论了p广义椭圆轮廓的p广义高斯分布的主成分表示。