glnorm {giniVarCI} | R Documentation |
Gini index for the Log Normal distribution with user-defined standard deviations
Description
Calculates the Gini indices for the Log Normal distribution with standard deviations (
sdlog
).
Usage
glnorm(sdlog)
Arguments
sdlog |
A vector of positive real numbers specifying standard deviations |
Details
The Log Normal distribution with mean , standard deviation
on the log scale (argument
sdlog
) and denoted as , has a probability density function given by (Kleiber and Kotz, 2003; Johnson et al., 1995)
and a cumulative distribution function given by
where and
is the cumulative distribution function of a standard Normal distribution.
The Gini index can be computed as
Value
A numeric vector with the Gini indices. A NA
is returned when a standard deviation is non-numeric or non-positive.
Note
The Gini index of the logNormal distribution does not depend on the mean 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
ggamma
, gpareto
, gchisq
, gweibull
Examples
# Gini index for the Log Normal distribution with standard deviation 'sdlog = 2'.
glnorm(sdlog = 2)
# Gini indices for the Log Normal distribution with different standard deviations.
glnorm(sdlog = c(0.2, 0.5, 1:3))