Kaniadakis Gamma distribution

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.

Definitions

Probability density function The Kaniadakis κ-Gamma distribution has the following probability density function:

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 .

Properties

Moments and mode The κ-Gamma distribution has moment of order given by

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:

Related distributions The κ-Gamma distributions is a generalization of: κ-Exponential distribution of type I, when ; Kaniadakis κ-Erlang distribution, when and positive integer. κ-Half-Normal distribution, when and ; A κ-Gamma distribution corresponds to several probability distributions when , such as: Gamma distribution, when ; Exponential distribution, when ; Erlang distribution, when and positive integer; Chi-Squared distribution, when and half integer; Nakagami distribution, when and ; Rayleigh distribution, when and ; Chi distribution, when and half integer; Maxwell distribution, when and ; Half-Normal distribution, when and ; Weibull distribution, when and ; Stretched Exponential distribution, when and ;

Kaniadakis Gamma distribution

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