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 (${\displaystyle 0<\lambda <1}$) or fermionic (${\displaystyle \lambda >1}$) character.

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 ${\displaystyle x\geq 0}$, where ${\displaystyle 0\leq |\kappa |<1}$ is the entropic index associated with the Kaniadakis entropy, ${\displaystyle \beta >0}$ is the rate parameter, ${\displaystyle \lambda >0}$, and ${\displaystyle \alpha >0}$ is the shape parameter.

The Logistic distribution is recovered as ${\displaystyle \kappa \rightarrow 0.}$

The cumulative distribution function of κ-Logistic is given by

valid for ${\displaystyle x\geq 0}$. The cumulative Logistic distribution is recovered in the classical limit ${\displaystyle \kappa \rightarrow 0}$.

The survival distribution function of κ-Logistic distribution is given by

valid for ${\displaystyle x\geq 0}$. The survival Logistic distribution is recovered in the classical limit ${\displaystyle \kappa \rightarrow 0}$.