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Kaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distribution

Christopoulos Dionysios, Baxevani, Anastassia

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URIhttp://purl.tuc.gr/dl/dias/E89E2747-D325-4B84-ABAF-EFEF66DA8A50-
Identifierhttps://doi.org/10.3390/e24101362-
Identifierhttps://www.mdpi.com/1099-4300/24/10/1362-
Languageen-
Extent22 pagesen
TitleKaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distributionen
CreatorChristopoulos Dionysiosen
CreatorΧριστοπουλος Διονυσιοςel
CreatorBaxevani, Anastassiaen
PublisherMDPIen
Content SummaryProbabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed 𝜅-Weibull distribution and weakest-link scaling theory, which makes the 𝜅-Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the 𝜅-lognormal probability distribution and calculate the generalized (power) mean of 𝜅-lognormal variables. The 𝜅-lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the 𝜅-deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2023-08-28-
Date of Publication2022-
SubjectKaniadakis exponentialen
SubjectΜodified lognormal distributionen
SubjectΕarthquake recurrence timesel
SubjectWeibull distributionen
SubjectPower-law tailen
SubjectPrecipitationen
SubjectFlow in random mediaen
SubjectTensile strengthen
Bibliographic CitationD. T. Hristopulos and A. Baxevani, “Kaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distribution,” Entropy, vol. 24, no. 10, Sep. 2022, doi: 10.3390/e24101362.en

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