README.md

In tukeyGH: Tukey's g-and-h Probability Distribution

Tukey’s g-and-h Probability Distribution

Presentation

The package provides distribution, density and quantile functions of the Tukey’s g-and-h probability distribution (Tukey 1977), as well as functions for random number generation, parameter estimation and testing.

In the current version of the package, the g-and-h distribution can be fitted through:

• indirect inference (Bee, Hambuckers, and Trapin 2019b)
• the quantile estimator (Hoaglin 1985)
• maximum likelihood (Bee, Hambuckers, and Trapin 2019a)

whereas the hypothesis (h=0) (which makes the g-and-h distribution, a g distribution) is tested by means of the log-likelihood ratio test procedure proposed in Bee et al. (2021).

An example

Fit the g-and-h distribution to dataset EPWS2014 on operational losses by means of indirect inference (Bee, Hambuckers, and Trapin 2019b), and quantile estimator (Hoaglin 1985):

library(tukeyGH)
data("EPWS2014")

modII <- fitGH(EPWS2014, method = "iinference")
summary(modII)

modQU <- fitGH(EPWS2014, method = "quantile")
summary(modQU)

modML <- fitGH(EPWS2014, method = "mle")
summary(modML)

rbind(QU = coef(modQU), II = coef(modII), ML = coef(modML))

References

Bee, M., J. Hambuckers, F. Santi, and L. Trapin. 2021. “Testing a Parameter Restriction on the Boundary for the G-and-H Distribution: A Simulated Approach.” *Computational Statistics*. .

Bee, M., J. Hambuckers, and L. Trapin. 2019a. “An Improved Approach for Estimating Large Losses in Insurance Analytics and Operational Risk Using the G-and-H Distribution.” DEM Working papers 2019/11. Department of Economics and Management, University of Trento.

———. 2019b. “Estimating Value-at-Risk for the G-and-H Distribution: An Indirect Inference Approach.” *Quantitative Finance* 19 (8): 1255–66. .

Hoaglin, D. C. 1985. “Exploring Data Tables, Trends, and Shapes.” In, edited by D. C. Hoaglin, F. Mosteller, and J. W. Tukey, 461–513. Wiley.

Tukey, J. W. 1977. “Modern Techniques in Data Analysis.”

tukeyGH documentation built on April 10, 2021, 9:06 a.m.