A general treatment of alternative expectation formulae

Liu, Yang

doi:10.1016/j.spl.2020.108863

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…for some c 1 > 0, all k ≥ 1 and all x ∈ R. Therefore, by the alternative expectation formula (see, for instance, [45]), we derive from ( 12) that…”

Section: Proof Of Part (V)mentioning

confidence: 99%

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Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

Leipus,

Šiaulys,

Danilenko

et al. 2024

Axioms

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This 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 variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided.

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“…for some c 1 > 0, all k ≥ 1 and all x ∈ R. Therefore, by the alternative expectation formula (see, for instance, [45]), we derive from ( 12) that…”

Section: Proof Of Part (V)mentioning

confidence: 99%

“…For any δ ∈ (0, c), using (2) and the alternative expectation formula (see [45], for instance), we obtain…”

Section: Heavy-tailed and Light-tailed Distributionsmentioning

confidence: 99%

Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

Leipus,

Šiaulys,

Danilenko

et al. 2024

Axioms

View full text Add to dashboard Cite

show abstract

“…For any δ ∈ (0, c), using (2) and the alternative expectation formula (see [39], for instance), we obtain…”

Section: Heavy-tailed and Light-tailed Distributionsmentioning

confidence: 99%

“…for some c 1 > 0, all k ≥ 1 and all x ∈ R. Therefore, by the alternative expectation formula (see, for instance, [39]), we derive from (10) that…”

Section: Proof Of Part (V)mentioning

confidence: 99%

Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions

Leipus,

Šiaulys,

Danilenko

et al. 2024

Preprint

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“…Proof. For completeness, we provide a direct proof; cf., [12]. For y ≥ 0, let χ y be the indicator function of the interval [0, y]; i.e., χ y (t) = 1 if 0 ≤ t ≤ y, and χ y…”

Section: (Russell and Sunmentioning

confidence: 99%

Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions

Edelmann¹,

Richards²,

Royen³

2022

Preprint

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The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial results have been derived in recent decades and we provide here further results on the problem. Most importantly, we establish a strong version of the Gaussian product inequality for multivariate gamma distributions in the case of nonnegative correlations, thereby extending a result recently derived by Genest and Ouimet [5]. Further, we show that the Gaussian product inequality holds with nonnegative exponents for all random vectors with positive components whenever the underlying vector is positively upper orthant dependent. Finally, we show that the Gaussian product inequality with negative exponents follows directly from the Gaussian correlation inequality.

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A general treatment of alternative expectation formulae

Cited by 7 publications

References 14 publications

Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions

Randomly Stopped Sums, Minima and Maxima for Heavy-tailed and Light-Tailed Distributions

Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions

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