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On degenerate Poisson random variable

Mathematical and Computer Modelling of Dynamical Systems
In this paper, we delve into the intricate properties of degenerate Poisson random variables, exploring their moment generating function, the law of large numbers, and the central limit theorem.
Mikyoung Ha, Suhyun Lee, Youngsoo Seol
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Fully degenerate Bell polynomials associated with degenerate Poisson random variables [PDF]

Open Mathematics, 2021
Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al.
Kim Hye Kyung
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POISSON APPROXIMATION FOR RANDOM SUMS OF GEOMETRIC RANDOM VARIABLES [PDF]

International Journal of Pure and Apllied Mathematics, 2013
In this paper, we determine bounds with different Poisson mean for the total variation distance between the distribution of random sums of in- dependent geometric random variables and an appropriate Poisson distribution. Two examples have been given to illustrate the results obtained.
K. Teerapabolarn
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Compound Poisson Approximations for Sums of Random Variables [PDF]

The Annals of Probability, 1986
We show that a sum of dependent random elements taking values in a semigroup is approximately compound Poisson when the elements are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson ...
Richard F. Serfozo
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Poisson approximation for independent geometric random variables [PDF]

International Mathematical Forum, 2007
The Stein-Chen method is used to derive two formulas of uniform and non-uniform bounds on Poisson approximation for a sum of n independent geometric random variables. Application of these formulas is illustrated with the Poisson approximation to the negative binomial distribution.
K. Teerapabolarn, P. Wongkasem
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On the implementation of maximum entropy sampling with unequal probabilities and without replacement [PDF]

MethodsX
Sampling with maximum entropy offers robustness to statistical inference based on randomization theory. However, there were no comprehensive, practical guides explaining how to implement maximum entropy sampling for finite populations with unequal ...
Philippe Aubry
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Poisson approximation for random sums of independent binomial random variables

Applied Mathematical Sciences, 2014
Let X1, ..., Xn be n independently distributed binomial random variables, each with probability P (Xi = k) = ( mi k ) pi q mi−k i for every k ∈ {0, 1, ...,mi}, where qi = 1− pi. Suppose that N is a positive integer-valued random variable and independent of Xi’s. Let SN = ∑N i=1Xi be the random sums of independent binomial random variables and Pλ denote
K. Teerapabolarn
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On the degenerate negative λ-binomial and Poisson random variables from degenerate special polynomials [PDF]

Mathematical and Computer Modelling of Dynamical Systems
In this paper, we investigate the theory and applications of negative λ-binomial random variable with parameter [Formula: see text] and Poisson random variable with parameter [Formula: see text].
Jongkyum Kwon, Sangbeom Park, Jin-Woo Park   +2 more
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STABLE POISSON CONVERGENCE FOR INTEGER-VALUED RANDOM VARIABLES [PDF]

Taiwanese Journal of Mathematics, 2013
In this paper, we obtain some stable Poisson Convergence Theorems for arrays of integer-valued dependent random variables. We prove that the limiting distribution is a mixture of Poisson distribution when the conditional second moments on a given $\sigma$-algebra of the sequence converge to some positive random variable.
Tsung‐Lin Cheng, Shun-Yi Yang
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Degenerate binomial and degenerate Poisson random variables [PDF]

, 2020
The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other things, we show that the rising factorial moments of the degenerate Poisson random variable with parameter are ...
Dae San Kim, Taekyun Kim
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