Tukey’s g-and-h Probability Distribution


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:

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):


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

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

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

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


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. https://doi.org/10.1007/s00180-021-01078-3.

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. https://doi.org/10.1080/14697688.2019.1580762.

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.”