The Kaniadakis Logistic distribution (also known as κ-Logisticdistribution) is a generalized version of the Logistic distribution associated with the Kaniadakis statistics. It is one example of a Kaniadakis distribution. The κ-Logistic probability distribution describes the population kinetics behavior of bosonic () or fermionic () character.
Definitions
Probability density function The Kaniadakis κ-Logistic distribution is a four-parameter family of continuous statistical distributions, which is part of a class of statistical distributions emerging from the Kaniadakis κ-statistics. This distribution has the following probability density function:
valid for , where is the entropic index associated with the Kaniadakis entropy, is the rate parameter, , and is the shape parameter.
The Logistic distribution is recovered as
Cumulative distribution function The cumulative distribution function of κ-Logistic is given by
valid for . The cumulative Logistic distribution is recovered in the classical limit .
Survival and hazard functions The survival distribution function of κ-Logistic distribution is given by
valid for . The survival Logistic distribution is recovered in the classical limit .
The hazard function associated with the κ-Logistic distribution is obtained by the solution of the following evolution equation:with , where is the hazard function:
The cumulative Kaniadakis κ-Logistic distribution is related to the hazard function by the following expression:
where is the cumulative hazard function. The cumulative hazard function of the Logistic distribution is recovered in the classical limit .
Related distributions The survival function of the κ-Logistic distribution represents the κ-deformation of the Fermi-Dirac function, and becomes a Fermi-Dirac distribution in the classical limit . The κ-Logistic distribution is a generalization of the κ-Weibull distribution when . A κ-Logistic distribution corresponds to a Half-Logistic distribution when , and . The ordinary Logistic distribution is a particular case of a κ-Logistic distribution, when .
Applications The κ-Logistic distribution has been applied in several areas, such as:
In quantum statistics, the survival function of the κ-Logistic distribution represents the most general expression of the Fermi-Dirac function, reducing to the Fermi-Dirac distribution in the limit .
See also
Giorgio Kaniadakis Kaniadakis statistics Kaniadakis distribution Kaniadakis κ-Exponential distribution Kaniadakis κ-Gaussian distribution Kaniadakis κ-Gamma distribution Kaniadakis κ-Weibull distribution Kaniadakis κ-Erlang distribution
References
External links Kaniadakis Statistics on arXiv.org