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 (

[1] 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:[1] valid for

is the entropic index associated with the Kaniadakis entropy,

is the rate parameter,

is the shape parameter.

The Logistic distribution is recovered as

The cumulative distribution function of κ-Logistic is given by valid for

The cumulative Logistic distribution is recovered in the classical limit

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:

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

The κ-Logistic distribution has been applied in several areas, such as: