金曼花的吸收时间、树长与甘贝尔分布

IF 0.4 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields Pub Date : 2015-01-01 DOI:10.15496/PUBLIKATION-9137

M. Möhle

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引用次数: 1

摘要

公式提供了累积量和时间的时刻T回到最近的共同祖先的金曼聚结。证明了T的第j个累积量和第j个矩是下列值的线性组合:ζ(2m)， m∈{0，…， bj/2c}，具有整数系数的黎曼ζ函数。该证明是基于一个具有可数多个初值的二维递归的解。在样本大小为n的情况下，导出了Kingman聚结的树长Ln的一个密切相关的强收敛结果。这些结果使我们有理由重新审视经典冈贝尔分布的矩和中心矩。

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Absorption Time and Tree Length of the Kingman Coalescent and the Gumbel Distribution

Formulas are provided for the cumulants and the moments of the time T back to the most recent common ancestor of the Kingman coalescent. It is shown that both the jth cumulant and the jth moment of T are linear combinations of the values ζ(2m), m ∈ {0, . . . , bj/2c}, of the Riemann zeta function ζ with integer coefficients. The proof is based on a solution of a two-dimensional recursion with countably many initial values. A closely related strong convergence result for the tree length Ln of the Kingman coalescent restricted to a sample of size n is derived. The results give reason to revisit the moments and central moments of the classical Gumbel distribution.

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来源期刊

Markov Processes and Related Fields STATISTICS & PROBABILITY-

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Markov Processes And Related Fields The Journal focuses on mathematical modelling of today''s enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc. Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.