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κ-Gamma distribution
Probability density function
shape (real)
rate (real)
Method of Moments

The Kaniadakis Generalized Gamma distribution (or κ-Generalized Gamma distribution) is a four-parameter family of continuous statistical distributions, supported on a semi-infinite interval [0,∞), which arising from the Kaniadakis statistics. It is one example of a Kaniadakis distribution. The κ-Gamma is a deformation of the Generalized Gamma distribution.


Probability density function

The Kaniadakis κ-Gamma distribution has the following probability density function:[1]

valid for , where is the entropic index associated with the Kaniadakis entropy, , is the scale parameter, and is the shape parameter.

The ordinary generalized Gamma distribution is recovered as : .

Cumulative distribution function

The cumulative distribution function of κ-Gamma distribution assumes the form:

valid for , where . The cumulative Generalized Gamma distribution is recovered in the classical limit .


Moments and mode

The κ-Gamma distribution has moment of order given by[1]

The moment of order of the κ-Gamma distribution is finite for .

The mode is given by:

Asymptotic behavior

The κ-Gamma distribution behaves asymptotically as follows:[1]

Related distributions

See also


  1. ^ a b c Kaniadakis, G. (2021-01-01). "New power-law tailed distributions emerging in κ-statistics (a)". Europhysics Letters. 133 (1): 10002. arXiv:2203.01743. Bibcode:2021EL....13310002K. doi:10.1209/0295-5075/133/10002. ISSN 0295-5075. S2CID 234144356.