The Kaniadakis Weibull distribution (or κ-Weibull distribution) is a
probability distribution arising as a generalization of the
Weibull distribution.[1][2] It is one example of a
Kaniadakis κ-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of
complex systems in seismology, economy, epidemiology, among many others.
Definitions
Probability density function
The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following
probability density function:[3]
valid for , where is the entropic index associated with the
Kaniadakis entropy, is the scale parameter, and is the shape parameter or
Weibull modulus.
A κ-Weibull distribution corresponds to a κ-deformed Rayleigh distribution when and a
Rayleigh distribution when and .
Applications
The κ-Weibull distribution has been applied in several areas, such as:
In
economy, for analyzing
personal income models, in order to accurately describing simultaneously the income distribution among the richest part and the great majority of the population.[1][4][5]
In
seismology, the κ-Weibull represents the statistical distribution of magnitude of the earthquakes distributed across the Earth, generalizing the
Gutenberg–Richter law,[6] and the interval distributions of seismic data, modeling extreme-event return intervals.[7][8]
In
epidemiology, the κ-Weibull distribution presents a universal feature for epidemiological analysis.[9]
The Kaniadakis Weibull distribution (or κ-Weibull distribution) is a
probability distribution arising as a generalization of the
Weibull distribution.[1][2] It is one example of a
Kaniadakis κ-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of
complex systems in seismology, economy, epidemiology, among many others.
Definitions
Probability density function
The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following
probability density function:[3]
valid for , where is the entropic index associated with the
Kaniadakis entropy, is the scale parameter, and is the shape parameter or
Weibull modulus.
A κ-Weibull distribution corresponds to a κ-deformed Rayleigh distribution when and a
Rayleigh distribution when and .
Applications
The κ-Weibull distribution has been applied in several areas, such as:
In
economy, for analyzing
personal income models, in order to accurately describing simultaneously the income distribution among the richest part and the great majority of the population.[1][4][5]
In
seismology, the κ-Weibull represents the statistical distribution of magnitude of the earthquakes distributed across the Earth, generalizing the
Gutenberg–Richter law,[6] and the interval distributions of seismic data, modeling extreme-event return intervals.[7][8]
In
epidemiology, the κ-Weibull distribution presents a universal feature for epidemiological analysis.[9]