Moments, Binomial Moments and Combinatorics

1997 ◽  
pp. 275-284
Author(s):  
Janos Galambos
Keyword(s):  
Binomial Moments

Detecting critical transitions in the case of moderate or strong noise by binomial moments

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Anwarud Din ◽  
Junhao Liang ◽  
Tianshou Zhou
Keyword(s):  
Critical Transitions ◽  
Binomial Moments

scholarly journals Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions

2020 ◽  
Vol 604 ◽  
pp. 92-128
Author(s):  
Eimear Byrne ◽  
Giuseppe Cotardo ◽  
Alberto Ravagnani
Keyword(s):  
Zeta Functions ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Binomial Moments

On explicit and Fréchet-optimal lower bounds

2002 ◽  
Vol 39 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Eugene Seneta ◽  
John Tuhao Chen
Keyword(s):  
Lower Bounds ◽  
Final Section ◽  
Sufficient Condition ◽  
Multiplicative Structure ◽  
Bivariate Case ◽  
Optimal Bounds ◽  
Explicit Bounds ◽  
Binomial Moments

Ease of computation of Fréchet-optimal lower bounds, given numerical values of the binomial moments Sij, i, j = 1, 2, is demonstrated. A sufficient condition is given for an explicit bivariate bound of Dawson-Sankoff structure to be Fréchet optimal. An example demonstrates that in the bivariate case even the multiplicative structure of the Sij does not guarantee a Dawson-Sankoff structure for Fréchet-optimal bounds. A final section is used to illuminate the nature of Fréchet optimality by using generalized explicit bounds. This note is a sequel to both Chen and Seneta (1995) and Chen (1998).

Multivariate Bonferroni-type lower bounds

1996 ◽  
Vol 33 (3) ◽  
pp. 729-740 ◽  
Author(s):  
Tuhao Chen ◽  
E. Seneta
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Indicator Functions ◽  
Binomial Moments

We derive multivariate Sobel–Uppuluri–Galambos-type lower bounds for the probability that at least a1 and at least a2, and for the probability that exactly a1 and a2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.

scholarly journals Bivariate Binomial Moments and Bonferroni-Type Inequalities

2016 ◽  
Vol 19 (1) ◽  
pp. 331-348
Author(s):  
Qin Ding ◽  
Eugene Seneta
Keyword(s):  
Binomial Moments

scholarly journals Probability distributions with binomial moments

2014 ◽  
Vol 17 (02) ◽  
pp. 1450014 ◽  
Author(s):  
Wojciech Młotkowski ◽  
Karol A. Penson
Keyword(s):  
Probability Distributions ◽  
Elementary Function ◽  
Positive Definite ◽  
Probability Measures ◽  
Bernoulli Distribution ◽  
Absolutely Continuous ◽  
Free Convolution ◽  
Meijer G Function ◽  
Convolution Powers ◽  
Binomial Moments

We prove that the binomial sequence [Formula: see text] is positive definite if and only if either p ≥ 1, -1 ≤ r ≤ p - 1 or p ≤ 0, p - 1 ≤ r ≤ 0 and that the Raney sequence [Formula: see text] is positive definite if and only if either p ≥ 1, 0 ≤ r ≤ p or p ≤ 0, p - 1 ≤ r ≤ 0 or else r = 0. The corresponding probability measures are denoted by ν(p, r) and μ(p, r) respectively. We prove that if p > 1 is rational and -1 < r ≤ p - 1 then the measure ν(p, r) is absolutely continuous and its density Vp,r(x) can be represented as Meijer G-function. In some cases Vp,r is an elementary function. We show that for p > 1 the measures ν(p,-1) and ν(p,0) are certain free convolution powers of the Bernoulli distribution.

Tandem queues with bulk arrivals, infinitely many servers and correlated service times

1997 ◽  
Vol 34 (1) ◽  
pp. 248-257 ◽  
Author(s):  
Ushio Sumita ◽  
Yasushi Masuda
Keyword(s):  
Service Time ◽  
Numerical Experiments ◽  
Queueing System ◽  
Tandem Queues ◽  
Renewal Equations ◽  
Occupancy Distribution ◽  
Service Times ◽  
Binomial Moments ◽  
Counterintuitive Result

A system of GIx/G/∞ queues in tandem is considered where the service times of a customer are correlated but the service time vectors for customers are independently and identically distributed. It is shown that the binomial moments of the joint occupancy distribution can be generated by a sequence of renewal equations. The distribution of the joint occupancy level is then expressed in terms of the binomial moments. Numerical experiments for a two-station tandem queueing system demonstrate a somewhat counterintuitive result that the transient covariance of the joint occupancy level decreases as the covariance of the service times increases. It is also shown that the analysis is valid for a network of GIx/SM/∞ queues.

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