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Sum of Poisson-Distributed Random Variables: A Convolution Method Approach
Journal of Applied Sciences and Environmental ManagementThis paper presents a two-parameter extension of the classical Poisson distribution, specifically tailored for rare event modeling. The proposed model is constructed as the sum of two independent Poisson random variables, using a convolution method ...
A. A. Ayenigba, O. M. Ajao, F. A. Okolie
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Dependence Modeling, 2023 The probability integral transform of a continuous random variable XX with distribution function FX{F}_{X} is a uniformly distributed random variable U=FX(X)U={F}_{X}\left(X). We define the angular probability integral transform (APIT) as θU=2πU=2πFX(X){\
Fernández-Durán Juan José +1 more
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Note on the bi-risk discrete time risk model with income rate two
Modern Stochastics: Theory and Applications, 2022 This article provides survival probability calculation formulas for bi-risk discrete time risk model with income rate two. More precisely, the possibility for the stochastic process $u+2t-{\textstyle\sum _{i=1}^{t}}{X_{i}}-{\textstyle\sum _{j=1}^{\lfloor
Andrius Grigutis, Artur Nakliuda
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Regularly distributed randomly stopped sum, minimum, and maximum
Nonlinear Analysis, 2020 Let {ξ1,ξ2,...} be a sequence of independent real-valued, possibly nonidentically distributed, random variables, and let η be a nonnegative, nondegenerate at 0, and integer-valued random variable, which is independent of {ξ1,ξ2,...}.
Jonas Sprindys, Jonas Šiaulys
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On the distribution of the sum of independent exponential-geometric random variables
, 2023 In this article, we derive exact expressions for the probability density function and cumulative distribution function of the sum of independent and non-identical exponential-geometric random variables.
AL-Zaydi, Areej; Taif University
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Random convolution of O-exponential distributions
Nonlinear Analysis, 2015 Assume that ξ1, ξ2, ... are independent and identically distributed non-negative random variables having the O-exponential distribution. Suppose that η is a nonnegative non-degenerate at zero integer-valued random variable independent of ξ1, ξ2, ... . In
Svetlana Danilenko, Jonas Šiaulys
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On the L_p-convergence for compound random sums of pairwise independent random variables
Tạp chí Khoa học và Công nghệA random sum is the sum of a random number of random variables, and it has attracted much attention from many researchers. Compound random sums are extensions of classical random sums, in which the random index is determined by the partial sum of ...
Phan Tri Kien
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Randomly stopped sums with exponential-type distributions
Nonlinear Analysis, 2017 Assume that {ξ1, ξ2, …} are independent and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at zero and integer-valued random variable, which is independent of {ξ1, ξ2, …}.
Svetlana Danilenko +2 more
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Logarithmic speeds for one-dimensional perturbed random walk in random environment
, 2007 We study the random walk in random environment on Z+ = f0; 1; 2; : : :g, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai's ...
Menshikov, MV +7 more
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An Algorithm for the Conditional Distribution of Independent Binomial Random Variables Given the Sum
MathematicsWe investigate Metropolis–Hastings (MH) algorithms to approximate the distribution of independent binomial random variables conditioned on the sum. Let Xi∼BIN(ni,pi). We want the distribution of [X1,…,Xk] conditioned on X1+⋯+Xk=n.
Kelly Ayres, Steven E. Rigdon
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