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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,…}. In this paper, we find conditions under which the distribution function of randomly stopped sum Sη=ξ1+ξ2+…+ξη
Jūratė Karasevičienė, Jonas Siaulys
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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. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken ...
Smithson, Michael, Shou, Yiyun
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Moments of Randomly Stopped Sums [PDF]
The Annals of Mathematical Statistics, 1965 1. Introduction. Let (Ω, F, P) be a probability space, let x 1 x 2, … be a sequence of random variables on Ω, and let F n be the σ-algebra generated by x 1, …, x n with F 0 = (φ,Ω). A stopping variable (of the sequence x 1, x2, …) is a random variable t on Ω with positive integer values such that the event [t = n] e F n for every n ≧ l.Let \( {S_n ...
Chow, Y. S. +2 more
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Lower Limits for Distribution Tails of Randomly Stopped Sums [PDF]
Theory of Probability & Its Applications, 2008 We study lower limits for the ratio F*τ̄(x)/ F̄(x) of tail distributions, where F*τ is a distribution of a sum of a random size τ of independent identically distributed random variables having a common distribution F, and a random variable τ does not depend on the summands. © 2008 Society for Industrial and Applied Mathematics.
Denisov, D. E. +2 more
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Randomly stopped sums with consistently varying distributions [PDF]
Modern Stochastics: Theory and Applications, 2016 Let $\{ _1, _2,\ldots\}$ be a sequence of independent random variables, and $ $ be a counting random variable independent of this sequence. We consider conditions for $\{ _1, _2,\ldots\}$ and $ $ under which the distribution function of the random sum $S_ = _1+ _2+\cdots+ _ $ belongs to the class of consistently varying distributions. In our
Kizinevič, Edita +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 random variable independent of $\{{X_{1}},{X_{2}},\dots \}$.
Remigijus Leipus, Jonas Šiaulys
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Regularly distributed randomly stopped sum, minimum, and maximum
Nonlinear Analysis: Modelling and Control, 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,...}. We consider conditions for {ξ1,ξ2,...} and η under which the distributions of the randomly stopped minimum, maximum, and
Jonas Sprindys, Jonas Šiaulys
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Randomly stopped maximum and maximum of sums with consistently varying distributions [PDF]
Modern Stochastics: Theory and Applications, 2017 Let $\{ _1, _2,\ldots\}$ be a sequence of independent random variables, and $ $ be a counting random variable independent of this sequence. In addition, let $S_0:=0$ and $S_n:= _1+ _2+\cdots+ _n$ for $n\geqslant1$. We consider conditions for random variables $\{ _1, _2,\ldots\}$ and $ $ under which the distribution functions of the random ...
Andrulytė, Ieva Marija +2 more
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Asymptotics of randomly stopped sums in the presence of heavy tails [PDF]
Bernoulli, 2010 We study conditions under which $P(S_ >x)\sim P(M_ >x)\sim E P( _1>x)$ as $x\to\infty$, where $S_ $ is a sum $ _1+...+ _ $ of random size $ $ and $M_ $ is a maximum of partial sums $M_ =\max_{n\le }S_n$. Here $ _n$, $n=1$, 2, ..., are independent identically distributed random variables whose common distribution is assumed to be ...
Denisov, Denis +2 more
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Randomly stopped sums with exponential-type distributions
Nonlinear Analysis: Modelling and Control, 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, …}. In this paper, we consider conditions for η and {ξ1, ξ2, …} under which the distribution of the random sum {ξ1 + ξ2 + … + ξη ...
Danilenko, Svetlana +2 more
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