dgh: Tukey's gh Distribution

In OpVaR: Statistical Methods for Modelling Operational Risk

Description

Density, distribution function, quantile function, and random generation for Tukey's gh distribution.

Usage

dgh(x, A, B, g, h, log = FALSE)
pgh(q, A, B, g, h, log.p = FALSE)
qgh(q, A, B, g, h, log.p =FALSE)
rgh(n, A, B, g, h)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations.
A	location parameter.
B	scale parameter, has to be positive.
g	skewness parameter.
h	kurtosis parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p)

Details

Tukey's gh distribution with location parameter A, scale parameter B, skewness parameter g, and kurtosis parameter h is obtained by transforming a standard normal variable X by

T(X)=A+B exp(h/2 X^2)(exp(gX)-1)/g

if g is not equal to zero, and else by

T(X)=A+B exp(h/2 X^2) X.

Value

dgh gives the density, pgh gives the distribution function, qgh gives the quantile function, and rgh generates random deviates.

The length of the result is determined by n for rgh, and is the length of the numerical arguments for the other function.

Author(s)

Linda Moestel

References

Tukey, J. W. (1960): The Practical Relationship between the Common Transformations of Counts of Amounts. Technical Report 36, Princeton University Statistical Techniques Research Group, Princeton.

Klein, I. and Fischer, M. (2002): Symmetrical gh-transformed Distributions. in S. Mittnek and I. Klein: Contributions to Modern Econometrics, Kluwer Academic Publishers.

Pfaelzner, F. (2017): Einsatz von Tukey-type Verteilungen bei der Quantifizierung von operationellen Risiken. MMasterthesis Friedrich-Alexander-University Erlangen-Nueremberg.

Examples

##Parameters  for a gh distribution
  A=500 
  B=3
  g=0.2
  h=0.5 
  
  hist(rgh(n=1000,A,B,g,h))
  curve(dgh(x,A,B,g,h),480,520)
  curve(pgh(x,A,B,g,h),480,520)
  curve(qgh(x,A,B,g,h),0,1)

Example output

OpVaR documentation built on Sept. 8, 2021, 5:07 p.m.