ggompertz {giniVarCI} | R Documentation |
Gini index for the Gompertz distribution with user-defined scale and shape parameters
Description
Calculate the Gini index for the Gompertz distribution with scale
parameter and
shape
parameter .
Usage
ggompertz(
scale = 1,
shape
)
Arguments
scale |
A positive real number specifying the scale parameter |
shape |
A positive real number specifying the shape parameter |
Details
The Gompertz distribution with scale
parameter ,
shape
parameter and denoted as
, where
and
, has a probability density function given by (Kleiber and Kotz, 2003; Johnson et al., 1995; Rodriguez, 1977; Yee, 2022)
and a cumulative distribution function given by
where .
The Gini index can be computed as
where is the quantile function of the Gompertz distribution, and
is the expectation of the distribution. If
scale
is not specified it assumes the default value of 1.
Value
A numeric value with the Gini index. A NA
is returned when a parameter is non-numeric or non-positive.
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
ggamma
, gbeta
, gchisq
, gpareto
Examples
# Gini index for the Gompertz distribution with 'scale = 1' and 'shape = 3'.
ggompertz(scale = 1, shape = 3)