gparetoII {giniVarCI} | R Documentation |
Gini index for the Pareto (II) distribution with user-defined location, scale and shape parameters
Description
Calculates the Gini index for the Pareto (II) distribution with location
parameter ,
scale
parameter and
shape
parameter .
Usage
gparetoII(
location = 0,
scale = 1,
shape = 1
)
Arguments
location |
A positive real number specifying the location parameter |
scale |
A positive real number specifying the scale parameter |
shape |
A positive real number specifying the shape parameter |
Details
The Pareto (II) distribution with location
parameter ,
scale
parameter ,
shape
parameter 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
where is the quantile function of the Pareto (II) distribution, and
is the expectation of the distribution. If
location
is not specified it assumes the default value of 0, and scale
and shape
assume the default value of 1. The Pareto (II) distribution is related to the Pareto (IV) distribution: .
Value
A numeric value with the Gini index. A NA
is returned when a parameter is non-numeric or positive, except the location parameter that can be equal to 0.
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
gpareto
, gparetoI
, gparetoIII
, gparetoIV
, gdagum
, gburr
, gfisk
Examples
# Gini index for the Pareto (II) distribution with parameters 'a = 1', 'b = 1' and 's = 3'.
gparetoII(location = 1, scale = 1, shape = 3)