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Randomly Stopped Sums: Models and Psychological Applications [PDF]
Frontiers in Psychology, 2014 This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable.
Michael eSmithson, Yiyun eShou
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Randomly Stopped Sums with Generalized Subexponential Distribution
Axioms, 2023 Let {ξ1,ξ2,…} be a sequence of independent possibly differently distributed random variables, defined on a probability space (Ω,F,P) with distribution functions {Fξ1,Fξ2,…}. Let η be a counting random variable independent of sequence {ξ1,ξ2,…}.
Jūratė Karasevičienė, Jonas Šiaulys
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Randomly stopped sums with consistently varying distributions [PDF]
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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A note on randomly stopped sums with zero mean increments
Modern Stochastics: Theory and Applications, 2023 In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum ${S_{\nu }}={X_{1}}+\cdots +{X_{\nu }}$ of independent identically distributed consistently varying random variables with zero mean, where ν is a counting ...
Remigijus Leipus, Jonas Šiaulys
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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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Randomly stopped maximum and maximum of sums with consistently varying distributions [PDF]
Modern Stochastics: Theory and Applications, 2017 Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables, and η be a counting random variable independent of this sequence. In addition, let $S_{0}:=0$ and $S_{n}:=\xi _{1}+\xi _{2}+\cdots +\xi _{n}$ for $n\geqslant 1$.
Ieva Marija Andrulytė +2 more
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Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions
AxiomsThis paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random ...
Remigijus Leipus +3 more
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A note on the asymptotics for the randomly stopped weighted sums
Nonlinear Analysis, 2018 Let {Xi , i ⩾ 1} be a sequence of identically distributed real-valued random variables with common distribution FX; let {θi , i ⩾ 1} be a sequence of identically distributed, nonnegative and nondegenerate at zero random variables; and let τ be a positive
Yang Yang, Xi Xi Shi, Xing Fang Huang
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AxiomsIn this paper, we find conditions under which distribution functions of randomly stopped minimum, maximum, minimum of sums and maximum of sums belong to the class of generalized subexponential distributions.
Jūratė Karasevičienė, Jonas Šiaulys
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A note on the tail behavior of randomly weighted and stopped dependent sums
Nonlinear Analysis, 2015 In this paper, we deal with the tail behavior of the maximum of randomly weighted and stopped sums. We assume that primary random variables (with a certain dependence structure) are identically distributed with heavy-tailed distribution function and ...
Lina Dindienė, Remigijus Leipus
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