gparetoIII {giniVarCI} | R Documentation |
Gini index for the Pareto (III) distribution with user-defined inequality parameters
Description
Calculate the Gini index for the Pareto (III) distribution with inequality
parameters .
Usage
gparetoIII(
inequality = 1
)
Arguments
inequality |
A vector of positive numbers in the |
Details
The Pareto (III) distribution with location parameter , scale parameter
,
inequality
parameter g
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 is
If inequality
is not specified it assumes the default value of 1. The Pareto (III) distribution is related to the Pareto (IV) distribution: .
Value
A numeric vector with the Gini indices. A NA
is returned when a inequality parameter is non-numeric or it is out of the interval .
Note
The Gini index of the Pareto (III) distribution does not depend on its location and scale parameters.
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
, gparetoII
, gparetoIV
, gdagum
, gburr
, gfisk
Examples
# Gini index for the Pareto (III) distribution with inequality parameter 'g = 0.3'.
gparetoIII(inequality = 0.3)
# Gini indices for the Pareto (III) distribution with different inequality parameters.
gparetoIII(inequality = seq(0.1, 0.9, by=0.1))