Results 11 to 20 of about 167,376 (263)
On The Equidistribution of Sums of Independent Random Variables [PDF]
Proceedings of the American Mathematical Society, 1953 Let X1, X2, ⋯ be a sequence of independent, real-valued random variables with a common distribution function \( F\left( x \right) = \Pr \left[ {{X_n}\underline \leqslant x} \right] \), and let \( {S_n} = {X_1} + \ldots + {X_n} \). We are going to show in an elementary manner that the sequence {S n } is “equi- distributed” on the line –∞
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A Novel Method for Increasing the Entropy of a Sequence of Independent, Discrete Random Variables
Entropy, 2015 In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions.
Mieczyslaw Jessa
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On the rate of convergence of Lp norms in the CLT for Poisson random sum
Lietuvos Matematikos Rinkinys, 2009 In the paper, we present the upper bound of Lp norm \deltaλ,p of the order λ-δ/2 for all 1 \leq p \leq ∞, in the central limit theorem for a standardized random sum (SNλ - ESNλ)/DSNλ , where SNλ = X1 + ··· + XNλ is the random sum of independent ...
Jonas Kazys Sunklodas
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Randomly stopped sums with consistently varying distributions
Modern Stochastics: Theory and Applications, 2016 Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables, and η be a counting random variable independent of this sequence. We consider conditions for $\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of ...
Edita Kizinevič +2 more
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On a Sum and Difference of Two Lindley Distributions
Revstat Statistical Journal, 2020 This paper investigates theoretical and practical aspects of two basic random variables constructed from Lindley distribution. The first one is defined as the sum of two independent random variables following the Lindley distribution (with the same ...
Christophe Chesneau +2 more
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A Global Limit Theorem for the Sum of N-Markov Bernoulli Random Variables [PDF]
The Egyptian Statistical Journal, 1991 A limit theorem is proved, in the Lp space, for the sum of n-Markov Bernoulli random variables. This result is a generalization of Gharib and Yehia [3], the integral limit theorem of a sequence of chain dependent trials [4], and the Berry-Essen theorem ...
Gharib M, Abdel Fattah M.
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Strong Approximations of Randomly Stopped Processes [PDF]
The Egyptian Statistical Journal, 1999 We study the limiting behavior of some important stochastic processes in weighted metrics based on independent identically distributed random variables when the sample size is random.
Abd-Elnaser Abd-Rabou
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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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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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