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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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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 minima and maxima with exponential-type distributions
Nonlinear Analysis, 2019 Let {ξ1, ξ2,...} be a sequence of independent real-valued and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at 0 and integer-valued random variable, which is independent of {ξ1, ξ2,...}.
Olena Ragulina, Jonas Šiaulys
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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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Extensions of Katz-Panjer families of discrete distributions
Revstat Statistical Journal, 2004 Let Nα, β, γ be a discrete random variable whose probability atoms {pn }n∈N satisfy f(n+1) f(n) = α + β E(U n 0 ) E(U n γ ) , n= 0, 1, ..., for some α, β ∈ R, where Uγ ⌢Uniform(γ, 1), γ ∈ (−1, 1].
Dinis D. Pestana , Sílvio F. Velosa
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Local probabilities of randomly stopped sums of power-law lattice random variables [PDF]
Lithuanian Mathematical Journal, 2019 Theorem 1 is improved a bit, misprints ...
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Neuroblastoma is the most common extracranial solid tumor in early childhood. Its clinical behavior is highly variable, ranging from spontaneous regression to fatal outcome despite intensive treatment. The International Society of Pediatric Oncology Europe Neuroblastoma Group (SIOPEN) Radiology and Nuclear Medicine Specialty Committees ...
Annemieke Littooij +11 more
wiley +1 more source
Function‐driven design of a surrogate interleukin‐2 receptor ligand
FEBS Letters, EarlyView.Interleukin (IL)‐2 signaling can be achieved and precisely fine‐tuned through the affinity, distance, and orientation of the heterodimeric receptors with their ligands. We designed a biased IL‐2 surrogate ligand that selectively promotes effector T and natural killer cell activation and differentiation. Interleukin (IL) receptors play a pivotal role in
Ziwei Tang +9 more
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Lower limits for distributions of randomly stopped sums
, 2007 We study lower limits for the ratio $\frac{\bar{F^{* }}(x)}{\bar F(x)}$ of tail distributions where $ F^{* }$ is a distribution of a sum of a random size $ $ of i.i.d. random variables having a common distribution $F$, and a random variable $ $ does not depend on summands.
Denisov, Denis +2 more
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