This work establishes Bernstein-type closed-form concentration inequalities for the beta distribution, with optimal variance proxy. For skewed distributions, these bounds are demonstrated to be more accurate then sub-gaussian and sub-gamma inequalities from prior works. The approach builds on the recursion obtained from a hyper-geometric representation of the central moments.

翻译：这项工作确立了贝塔分布的伯恩斯坦型封闭式浓度不平等,并有最佳差异替代物。 对于偏斜分布,这些界限被证明更为准确,而以前作品的偏斜分布则更准确,而以前作品的亚加西语和亚伽马语的不平等则更准确。 这种方法以从中心时段的超几何表示法中获得的循环为基础。