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Comments on the Bernoulli Distribution and Hilbe’s Implicit Extra-Dispersion
StatsFor decades, conventional wisdom maintained that binary 0–1 Bernoulli random variables cannot contain extra-binomial variation. Taking an unorthodox stance, Hilbe actively disagreed, especially for correlated observation instances, arguing that the ...
Daniel A. Griffith
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Euler's constant, sequences and some estimates [PDF]
Surveys in Mathematics and its Applications, 2013 We give a class of sequences with the argument of the logarithmic term modified and that converge quickly to a generalization of Euler's constant denoted by γ(a), i.e. the limit of the sequence (∑k=1n1/(a+k-1)-ln((a+n-1)/a)n∈ℕ, where a∈(0,+∞).
Alina Sîntămărian
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Zhejiang Daxue xuebao. Lixue ban, 2022 得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子Nh的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises，QBN）的加权表示；（2）Nh的谱表示，广义计数算子Nh以h-计数测度#h的值域为其点谱；（3）Nh的“对角化”表示，Nh可表示为L2(M)的标准正交基{Zσ；σ∈Γ}所生成的一维对角化正交投影算子的加权极限；（4）广义Skorohod积分-广义随机梯度表示，Nh可表示为互共轭算子δh和∇h的复合算子；（5）对N上的任意非负函数h ...
ZHOUYulan(周玉兰) +4 more
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Estimate of third Hankel determinant for a subfamily of analytic functions
Annals of the West University of Timisoara: Mathematics and Computer Science, 2023 In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions.
Shah Syed Ghoos Ali +4 more
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Discretized normal approximation by Stein's method
, 2014 We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution.
Fang, Xiao
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Fractional pure birth processes
, 2009 We consider a fractional version of the classical nonlinear birth process of which the Yule--Furry model is a particular case. Fractionality is obtained by replacing the first order time derivative in the difference-differential equations which govern ...
Orsingher, Enzo, Polito, Federico
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Poly-Bernoulli Numbers and Eulerian Numbers
, 2018 In this note we prove combinatorially some new formulas connecting poly-Bernoulli numbers with negative indices to Eulerian numbers.
Bényi, Beáta, Hajnal, Péter
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Journal of Fluid Science and Technology, 2016 The extended Bernoulli equation is formulated in an exact form for a microscopic and small Reynolds number Jeffery-Hamel flow in a two-dimensional convergent or divergent channel.
Toshihide FUJIKAWA +4 more
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Congruences for Bernoulli numbers and Bernoulli polynomials
Discrete Mathematics, 1997 The Bernoulli numbers and polynomials are defined by \(B_0=1\), \(\sum^{n-1}_{k=0}{n\choose k} B_k= 0\) \((n=2,3,\dots)\) and \(B_n(x)= \sum^n_{k=0}{n\choose k} B_{n-k} x^k\), respectively. Two basic congruences for Bernoulli numbers are the Kummer congruences (used in the theory of Fermat's last theorem) and the von Staudt-Clausen theorem. There exist
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Entropy theory for sofic groupoids I: the foundations [PDF]
, 2013 This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance.
Bowen, Lewis
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