Kaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distributionKaniadakis functions beyond statistical mechanics: weakest-link scaling, power-law tails, and modified lognormal distribution
Peer-Reviewed Journal Publication
Δημοσίευση σε Περιοδικό με Κριτές
2023-08-282022enProbabilistic 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.http://creativecommons.org/licenses/by/4.0/Entropy2410Hristopulos_et_al_Entropy_24(10)_2022.pdfChania [Greece]Library of TUC2023-08-28application/pdf1.3 MBfree
Christopoulos Dionysios
Χριστοπουλος Διονυσιος
Baxevani, Anastassia
MDPI
Kaniadakis exponential
Μodified lognormal distribution
Εarthquake recurrence times
Weibull distribution
Power-law tail
Precipitation
Flow in random media
Tensile strength