Kaniadakis logistic distribution
Probability distribution From Wikipedia, the free encyclopedia
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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Probability density function ![]() Plot of the κ-Logistic distribution for typical κ-values and . The case corresponds to the ordinary Logistic distribution. | |||
Cumulative distribution function ![]() Plots of the cumulative κ-Logistic distribution for typical κ-values and . The case corresponds to the ordinary Logistic case. | |||
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shape (real) rate (real) | ||
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CDF |
Definitions
Summarize
Perspective
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 .
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 .[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 .
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
External links
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