The Kaniadakis Logistic distribution (also known as ú-Logisticdistribution) is a generalized version of the Logistic distribution associated with the Kaniadakis statistics. It is one example of a Kaniadakis distribution. The ú-Logistic probability distribution describes the population kinetics behavior of bosonic () or fermionic () character.
The Kaniadakis ú-Logistic distribution is a four-parameter family of continuous statistical distributions, which is part of a class of statistical distributions emerging from the Kaniadakis ú-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
The cumulative distribution function of ú-Logistic is given by
valid for . The cumulative Logistic distribution is recovered in the classical limit .
The survival distribution function of ú-Logistic distribution is given by
valid for . The survival Logistic distribution is recovered in the classical limit .
The hazard function associated with the ú-Logistic distribution is obtained by the solution of the following evolution equation:<blockquote></blockquote>with , where is the hazard function:
The cumulative Kaniadakis ú-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 ú-Logistic distribution has been applied in several areas, such as: