# dgh: Tukey's gh Distribution In OpVaR: Statistical Methods for Modeling Operational Risk

## Description

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

## Usage

 ```1 2 3 4``` ```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.

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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```##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) ```

OpVaR documentation built on May 29, 2018, 9:04 a.m.