Stochastic Order for a Multivariate Uniform Distributions Family

Catana, Luigi-Ionut; Răducan, Anişoara Maria

doi:10.3390/math8091410

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…There are several papers in which the authors compare random variables from the point of view of residual entropies: for Shannon residual entropy, see [30][31][32]; for Rényi residual entropy, see [33,34]; for Varma residual entropy, see [35]; and for Awad-Varma residual entropy, see [36]. Other orders between random variables can be found in [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Order Properties Concerning Tsallis Residual Entropy

Sfetcu,

Preda

2024

Mathematics

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With the help of Tsallis residual entropy, we introduce Tsallis quantile entropy order between two random variables. We give necessary and sufficient conditions, study closure and reversed closure properties under parallel and series operations and show that this order is preserved in the proportional hazard rate model, proportional reversed hazard rate model, proportional odds model and record values model.

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Section: Introductionmentioning

confidence: 99%

Order Properties Concerning Tsallis Residual Entropy

Sfetcu,

Preda

2024

Mathematics

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Stochastic orders of log-epsilon-skew-normal distributions

Catana

2022

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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The log-epsilon-skew-normal distributions family is generalized class of log-normal distribution. Is widely used to model non-negative data in many areas of applied research. We give necessary and/or sufficient conditions for some stochastic orders of log-epsilon-skew-normal distributions. Also, we give sufficient conditions for orders of moments and Gini indexes. Finally, it is presented a real data application.

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A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes

Catana

Preda

2022

Mathematics

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In this article, we introduce and study a new stochastic order of multivariate distributions, namely, the conditional likelihood ratio order. The proposed order and other stochastic orders are analyzed in the case of a bivariate exponential distributions family. The theoretical results obtained are applied for studying the reliability of bridges affected by earthquakes. The conditional likelihood ratio order involves the multivariate stochastic ordering; it resembles the likelihood ratio order in the univariate case but is much easier to verify than the likelihood ratio order in the multivariate case. Additionally, the likelihood ratio order in the multivariate case implies this ordering. However, the conditional likelihood ratio order does not imply the weak hard rate order, and it is not an order relation on the multivariate distributions set. The new conditional likelihood ratio order, together with the likelihood ratio order and the weak hazard rate order, were studied in the case of the bivariate Marshall–Olkin exponential distributions family, which has a lack of memory type property. At the end of the paper, we also presented an application of the analyzed orderings for this bivariate distributions family to the study of the effects of earthquakes on bridges.

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Stochastic Order for a Multivariate Uniform Distributions Family

Abstract: In this article we give sufficient conditions for stochastic order of multivariate uniform distributions on closed convex sets.

Cited by 3 publications

References 15 publications

Order Properties Concerning Tsallis Residual Entropy

Order Properties Concerning Tsallis Residual Entropy

Stochastic orders of log-epsilon-skew-normal distributions

A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes

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