The Kaniadakis Gaussian distribution (also known as κ-Gaussian distribution) is a probability distribution which arises as a generalization of the Gaussian distribution from the maximization of the Kaniadakis entropy under appropriated constraints. It is one example of a Kaniadakis κ-distribution. The κ-Gaussian distribution has been applied successfully for describing several complex systems in economy,[1] geophysics,[2] astrophysics, among many others.
The Kaniadakis κ-Error function (or κ-Error function) is a one-parameter generalization of the ordinary error function defined as:[3]
Although the error function cannot be expressed in terms of elementary functions, numerical approximations are commonly employed.
For a random variableX distributed according to a κ-Gaussian distribution with mean 0 and standard deviation , κ-Error function means the probability that X falls in the interval .
Applications
The κ-Gaussian distribution has been applied in several areas, such as:
In economy, the κ-Gaussian distribution has been applied in the analysis of financial models, accurately representing the dynamics of the processes of extreme changes in stock prices.[4]
In astrophysics, stellar-residual-radial-velocity data have a Gaussian-type statistical distribution, in which the K index presents a strong relationship with the stellar-cluster ages.[7][8]
In nuclear physics, the study of Doppler broadening function in nuclear reactors is well described by a κ-Gaussian distribution for analyzing the neutron-nuclei interaction.[9][10]