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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. | |||
Parameters |
shape ( real) rate ( real) | ||
---|---|---|---|
Support | |||
CDF |
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]
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
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:
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 .
The κ-Logistic distribution has been applied in several areas, such as:
![]() | The topic of this article may not meet Wikipedia's
general notability guideline. (February 2023) |
This article relies largely or entirely on a
single source. (July 2022) |
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. | |||
Parameters |
shape ( real) rate ( real) | ||
---|---|---|---|
Support | |||
CDF |
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]
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
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:
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 .
The κ-Logistic distribution has been applied in several areas, such as: