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Kaniadakis logistic distribution

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Kaniadakis logistic distribution
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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.[1]

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Definitions

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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:[1]

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 .

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  • 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 .[1]
  • 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 .
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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 .[2][3][4]

See also

References

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