# gsample: Samples from a set of continuous probability distributions... In giniVarCI: Gini Indices, Variances and Confidence Intervals for Finite and Infinite Populations

 gsample R Documentation

## Samples from a set of continuous probability distributions with user-defined Gini indices

### Description

Draws samples from a continuous probability distribution with Gini indices set by the user.

### Usage

gsample(
n,
gini,
distribution = c("pareto", "dagum", "lognormal", "fisk", "weibull", "gamma",
"chisq", "frechet"),
scale = 1,
meanlog = 0,
shape2.p = 1,
location = 0
)

### Arguments

 n An integer specifying the sample(s) size. gini A numeric vector of values between 0 and 1, indicating the Gini indices for the continuous distribution from which samples are generated. distribution A character string specifying the continuous probability distribution to be used to generate the sample. Possible values are "pareto", "dagum", "lognormal", "fisk", "weibull", "gamma", "chisq" and "frechet" for the Pareto, Dagum, logNormal, Fisk (Log-logistic), Weibull, Gamma, Chi-Squared and Frechet distributions, respectively. scale The scale parameter for the Pareto, Dagum, Fisk, Weibull, Gamma and Frechet distributions. The default value is scale = 1. meanlog The mean for the logNormal distribution on the log scale. The default value is meanlog = 0. shape2.p The scale parameter p for the Dagum distribution. The default value is shape2.p = 1. location The location parameter for the Frechet distribution. The default value is location = 0.

### Details

For each continuous probability distribution, parameters involved in the theoretical formulation of the Gini index (G) are selected such that G takes the values set in the argument gini. Additional parameters required in the distribution can be set by the user, and default values are provided. scale is the scale parameter for the Pareto, Dagum, Fisk, Weibull, Gamma and Frechet distributions, meanlog is the mean for the Lognormal distribution on the log scale, shape2.p is the scale parameter p for the Dagum distribution, and location is the location parameter for the Frechet distribution. Additional information for the continuous probability distributions used by this function can be seen in Kleiber and Kotz (2003), Johnson et al. (1995) and Yee (2022).

### Value

A numeric vector (or matrix of order n \times size(gini)) with the samples by columns extracted from the continuous probability distribution stated in distribution and the Gini indices corresponding to the vector gini.

### Note

Underestimation problems may appear for large heavy-tailed distributions (Pareto, Dagum, Lognormal, Fisk and Frechet) and large values of gini. A larger sample size may solve/minimize this problem.

### 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.

gpareto, gdagum, glnorm, gfisk, gweibull, ggamma, gchisq, gfrechet

### Examples

# Sample from the Pareto distribution and parameter selected such that the Gini index is 0.3.
gsample(n = 10, gini = 0.3, "pareto")

# Samples from the Pareto distribution and gini indices 0.2 and 0.5.
gsample(n = 10, gini = c(0.2,0.5), "par", scale = 2)

# Samples from the Lognormal distribution and gini indices 0.2 and 0.5.
gsample(n = 10, gini = c(0.2,0.5), "lognormal", meanlog = 5)

# Samples from the Dagum distribution and gini indices 0.2 and 0.5.
gsample(n = 10, gini = c(0.2,0.5), "dagum")

# Samples from the Fisk (Log-logistic) distribution and gini indices 0.3 and 0.6.
gsample(n = 10, gini = c(0.3,0.6), "fisk")

# Sample from the Weibull distribution and parameter selected such that the Gini index is 0.2.
gsample(n = 10, gini = 0.2, "weibull")

# Sample from the Gamma distribution and parameter selected such that the Gini index is 0.3.
gsample(n = 10, gini = 0.2, "gamma")

# Samples from the Chi-Squared distribution and gini indices 0.3 and 0.6..
gsample(n = 10, gini = c(0.3,0.6), "chi")

# Samples from the Frechet distribution and gini indices 0.3 and 0.6.
gsample(n = 10, gini = c(0.3,0.6), "fre")

giniVarCI documentation built on May 29, 2024, 3:36 a.m.