ggamma {giniVarCI} | R Documentation |
Gini index for the Gamma distribution with user-defined shape parameter
Description
Calculates the Gini indices for the Gamma distribution with shape
parameters .
Usage
ggamma(shape)
Arguments
shape |
A vector of positive real numbers specifying the shape parameters |
Details
The Gamma distribution with shape
parameter , scale parameter
and denoted as
, where
and
, has a probability density function given by (Kleiber and Kotz, 2003; Johnson et al., 1995)
and a cumulative distribution function given by
where , the gamma function is defined by
and the lower incomplete gamma function is given by
The Gini index can be computed as
The Gamma distribution is related to the Chi-squared 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 Gamma 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.
See Also
gchisq
, gf
, gbeta
, gweibull
, glnorm
Examples
# Gini index for the Gamma distribution with 'shape = 1'.
ggamma(shape = 1)
# Gini indices for the Gamma distribution and different shape parameters.
ggamma(shape = 1:10)