广义Maxwell-Boltzmann，Bose-Einstein，Fermi-Dirac和Acharya-Swamy统计量与Polya瓮模型
Generalized Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac and Acharya-Swamy Statistics and the Polya Urn Model
摘要：
通过组合推理得到了Maxwell-Boltzmann、Bose-Einstein和Fermi-Dirac统计量的广义概率分布，其中每个能级$i$的源概率$q_i$不等.对于等概率简并子能级，这些减少到布里渊在1930年给出的那些，更常见的是作为每个统计量的统计权重。这些分布和相应的交叉熵（发散）函数被证明是波利亚瓮模型的特殊情况，既不涉及独立也不涉及同分布（“ninid”）采样。最可能的波利亚分布包含Acharya-Swamy中间统计量。
英文摘要：
Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source probabilities $q_i$ for each level $i$, are obtained by combinatorial reasoning. For equiprobable degenerate sublevels, these reduce to those given by Brillouin in 1930, more commonly given as a statistical weight for each statistic. These distributions and corresponding cross-entropy (divergence) functions are shown to be special cases of the Pólya urn model, involving neither independent nor identically distributed ("ninid") sampling. The most probable Pólya distribution contains the Acharya-Swamy intermediate statistic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
