Characterization of a general class of tail probability distributions

Cadena, Meitner; Kratz, Marie; Omey, Edward

doi:10.1016/j.spl.2019.108553

“…In this paper we study the product of r.vs whose tail functions belong to the class M(H, ρ), introduced by Cadena et al [9]. For a function H, such that H(x) → ∞, x → ∞, and given −∞ < ρ < ∞, the class M(H, ρ) consists of functions U such that lim…”

Section: Introductionmentioning

confidence: 99%

Revisiting the Product of Random Variables

Cadena

¹

,

Omey

²

,

Vesilo

³

2022

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For a large class of distribution functions we study properties of the product of random variables X and Y . We take into account the dependency structure between X and Y by making assumptions about the asymptotic equality P(X > x|Y = y) ∼ h(y)P(X > x) as x → ∞, uniformly for y in the range of Y . As particular consequences, some well-known results concerning the product of random variables are reviewed, among them the Breiman's theorem. An application is made in the case where the dependence between X and Y is characterized by asymptotic conditions on their copula.

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“…Nevertheless, the problem has a number of important theoretical applications arising in the theory of probability, stochastic processes and their real life applications (e.g. [1,6,8]).…”

Section: Introductionmentioning

confidence: 99%

“…Bingham, Goldie and Teugels [2]). Recently, Cadena, Kratz and Omey [5] described a new class of functions that covers the class of functions regularly varying at infinity, and in the other recent paper of these authors [6] that new class of functions was used for characterization of the tail probability distribution functions under general settings. Taking that new class into consideration enables us to further reconsider and develop the earlier tests on convergence/divergence of positive series.…”

Section: Introductionmentioning

confidence: 99%

A new test for convergence of positive series

Abramov¹,

Cadena

²

,

Omey

³

2021

Publ Inst Math (Belgr)

Self Cite

1

0

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“…Nowadays there is a large variety of tests on convergence/divergence of positive series, and most of the existing practical problems that involve positive series are resolved. Nevertheless, the problem has a number of important theoretical applications arising in the theory of probability, stochastic processes and their real life applications (e. g. [1,6,8]).…”

Section: Introductionmentioning

confidence: 99%

“…Bingham, Goldie and Teugels [2]). Recently, Cadena, Kratz and Omey [5] described a new class of functions that covers the class of functions regularly varying at infinity, and in the other recent paper of these authors [6] that new class of functions was used for characterization of the tail probability distribution functions under general settings. Taking that new class into consideration enables us to further reconsider and develop the earlier tests on convergence/divergence of positive series.…”

Section: Introductionmentioning

confidence: 99%