A bimodal model for extremes data

Otiniano, Cira E. G.; Sousa, Bianca; Vila, Roberto; Bourguignon, Marcelo

doi:10.1007/s10651-023-00566-7

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Let us introduce our suggested generalization of the Gumbel distribution left open by [15] in the following way. Considering the transformation,…”

Section: Resultsmentioning

confidence: 99%

“…However, some lead to non-identifiable models because of observationally equivalent parameterizations [12]. There are other closely related models such as the exponentiated Gumbel Type-2 [13], the Kumaraswamy generalized exponentiated Gumbel type-2 [14], the bimodal generalized extreme value (GEV) [15], and a bimodal Gumbel distribution applied to environmental data [16]. However, the disadvantage of the latter model is that its cumulated distribution function does not have a simple closed form.…”

Section: Introductionmentioning

confidence: 99%

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Bridging Extremes: The Invertible Bimodal Gumbel Distribution

Otiniano,

Silva,

Matsushita

et al. 2023

Entropy

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This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.

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“…Let us introduce our suggested generalization of the Gumbel distribution left open by [15] in the following way. Considering the transformation,…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

Otiniano,

Silva,

Matsushita

et al. 2023

Entropy

Self Cite

View full text Add to dashboard Cite

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bgev: Bimodal GEV Distribution with Location Parameter

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2024

CRAN: Contributed Packages

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Estimation of P(X < Y) Stress–Strength Reliability Measures for a Class of Asymmetric Distributions: The Case of Three-Parameter p-Max Stable Laws

Quintino,

Rathie,

Ozelim

et al. 2024

Symmetry

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Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, we derive stress–strength reliability formulas of the type P(X<Y) when both X and Y follow p-max stable laws with three parameters, which are inherently asymmetric. The new relations are given in terms of extreme-value H-functions and have been obtained under fewer parameter restrictions when compared to similar results in the literature. We estimate the parameters of the p-max stable laws by a stochastic optimization method and the stress–strength probability by a maximum likelihood procedure. The performance of the analytical models is evaluated through simulations and real-life dataset modeling.

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A bimodal model for extremes data

Cited by 3 publications

References 20 publications

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

bgev: Bimodal GEV Distribution with Location Parameter

Estimation of P(X < Y) Stress–Strength Reliability Measures for a Class of Asymmetric Distributions: The Case of Three-Parameter p-Max Stable Laws

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