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κ-Weibull distribution
Probability density function
Cumulative distribution function
Parameters
rate shape (real) rate (real)
Support
PDF
CDF
Quantile
Median
Mode
Method of moments
The Kaniadakis Weibull distribution (or κ-Weibull distribution) is a probability distribution arising as a generalization of the Weibull distribution.[1][2] It is one example of a Kaniadakis κ-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of complex systems in seismology, economy, epidemiology, among many others.
^Clementi, F.; Gallegati, M.; Kaniadakis, G. (2007). "κ-generalized statistics in personal income distribution". The European Physical Journal B. 57 (2): 187–193. arXiv:physics/0607293. Bibcode:2007EPJB...57..187C. doi:10.1140/epjb/e2007-00120-9. ISSN 1434-6028. S2CID 15777288.
^Clementi, F.; Di Matteo, T.; Gallegati, M.; Kaniadakis, G. (2008). "The -generalized distribution: A new descriptive model for the size distribution of incomes". Physica A: Statistical Mechanics and Its Applications. 387 (13): 3201–3208. arXiv:0710.3645. doi:10.1016/j.physa.2008.01.109. S2CID 2590064.
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![{\displaystyle \beta ^{-1/\alpha }{\Bigg [}\ln _{\kappa }{\Bigg (}{\frac {1}{1-F_{\kappa }}}{\Bigg )}{\Bigg ]}^{1/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b52bba751bd8c84676ad4ea48dde2c717b197e4)
![{\displaystyle \beta ^{-1/\alpha }{\Bigg (}{\frac {\alpha ^{2}+2\kappa ^{2}(\alpha -1)}{2\kappa ^{2}(\alpha ^{2}-\kappa ^{2})}}{\sqrt {1+{\frac {4\kappa ^{2}(\alpha ^{2}-\kappa ^{2})(\alpha -1)^{2}}{[\alpha ^{2}+2\kappa ^{2}(\alpha -1)]^{2}}}}}-1{\Bigg )}^{1/2\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e553db64cc7631a2e8bd64f6d31b670a13ffb52b)
