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

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

α ν − 1

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

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]