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