[1] There are several families of Kaniadakis distributions related to different constraints used in the maximization of the Kaniadakis entropy, such as the κ-Exponential distribution, κ-Gaussian distribution, Kaniadakis κ-Gamma distribution and κ-Weibull distribution.

The κ-distributions have been applied for modeling a vast phenomenology of experimental statistical distributions in natural or artificial complex systems, such as, in epidemiology,[2] quantum statistics,[3][4][5] in astrophysics and cosmology,[6][7][8] in geophysics,[9][10][11] in economy,[12][13][14] in machine learning.

[15] The κ-distributions are written as function of the κ-deformed exponential, taking the form enables the power-law description of complex systems following the consistent κ-generalized statistical theory.,[16][17] where

is the Kaniadakis κ-exponential function.

The κ-distribution becomes the common Boltzmann distribution at low energies, while it has a power-law tail at high energies, the feature of high interest of many researchers.

The Kaniadakis distribution of Type IV (or κ-Distribution Type IV) is a three-parameter family of continuous statistical distributions.

[1] The κ-Distribution Type IV distribution has the following probability density function: valid for

is the entropic index associated with the Kaniadakis entropy,

The cumulative distribution function of κ-Distribution Type IV assumes the form: The κ-Distribution Type IV does not admit a classical version, since the probability function and its cumulative reduces to zero in the classical limit

of the κ-Distribution Type IV is finite for