gfisk {giniVarCI} | R Documentation |
Gini index for the Fisk (Log Logistic) distribution with user-defined shape parameters
Description
Calculates the Gini indices for the Fisk (Log Logistic) distribution with shape parameters (
shape1.a
).
Usage
gfisk(shape1.a)
Arguments
shape1.a |
A vector of positive real numbers specifying shape parameters |
Details
The Fisk (Log Logistic) distribution with scale parameter , shape parameter
(argument
shape1.a
) and denoted as , where
and
, has a probability density function given by (Kleiber and Kotz, 2003; Johnson et al., 1995; Yee, 2022)
and a cumulative distribution function given by
where .
The Gini index can be computed as
The Fisk (Log Logistic) distribution is related to the Dagum distribution: .
Value
A numeric vector with the Gini indices. A NA
is returned when a shape parameter is non-numeric or non-positive.
Note
The Gini index of the Fisk (Log Logistic) distribution does not depend on its scale parameter.
Author(s)
Juan F Munoz jfmunoz@ugr.es
Jose M Pavia pavia@uv.es
Encarnacion Alvarez encarniav@ugr.es
References
Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 14. Wiley, New York.
Yee, T. W. (2022). VGAM: Vector Generalized Linear and Additive Models. R package version 1.1-7, https://CRAN.R-project.org/package=VGAM.
See Also
gdagum
, gburr
, gpareto
, ggompertz
Examples
# Gini index for the Fisk distribution with a shape parameter 'a = 2'.
gfisk(shape1.a = 2)
# Gini indices for the Fisk distribution and different shape parameters.
gfisk(shape1.a = 1:10)