发表机构
Technical University of Braunschweig（布伦瑞克工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出递归重叠伯努利分布族，插值于二项分布与非重叠乘积分布，推导矩公式并猜想熵凹性，在极端情形证明并数值支持。
AI 中文摘要
我们引入一族由左右嵌入且带有重叠而递归生成的有限概率分布。该构造在经典二项分布与非重叠伯努利乘积分布之间进行插值。我们推导了期望、方差以及高阶矩生成函数的显式公式，并提出了一个断言香农熵是凹的猜想。该猜想在两个极端情形下得到证明，并通过对大量重叠序列的符号计算得到支持。
英文摘要
We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.
