gweibull {giniVarCI} | R Documentation |
Gini index for the Weibull distribution with user-defined shape parameters
Description
Calculate the Gini indices for the Weibull distribution with shape
parameters .
Usage
gweibull(shape)
Arguments
shape |
A vector of positive real numbers specifying shape parameters |
Details
The Weibull 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; Yee, 2022)
and a cumulative distribution function given by
where .
The Gini index can be computed as
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 Weibull 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
Examples
# Gini index for the Weibull distribution with 'shape = 1'.
gweibull(shape = 1)
# Gini indices for the Weibull distribution and different shape parameters.
gweibull(shape = 1:10)