# dist-sgh: Standardized Generalized Hyperbolic Distribution In fBasics: Rmetrics - Markets and Basic Statistics

## Description

Density, distribution function, quantile function and random generation for the standardized generalized hyperbolic distribution.

## Usage

 ```1 2 3 4``` ```dsgh(x, zeta = 1, rho = 0, lambda = 1, log = FALSE) psgh(q, zeta = 1, rho = 0, lambda = 1) qsgh(p, zeta = 1, rho = 0, lambda = 1) rsgh(n, zeta = 1, rho = 0, lambda = 1) ```

## Arguments

 `zeta, rho, lambda` shape parameter `zeta` is positive, skewness parameter `rho` is in the range (-1, 1). `log` a logical flag by default `FALSE`. If TRUE, log values are returned. `n` number of observations. `p` a numeric vector of probabilities. `x, q` a numeric vector of quantiles.

## Details

The generator `rsgh` is based on the GH algorithm given by Scott (2004).

## Value

All values for the `*sgh` functions are numeric vectors: `d*` returns the density, `p*` returns the distribution function, `q*` returns the quantile function, and `r*` generates random deviates.

All values have attributes named `"param"` listing the values of the distributional parameters.

Diethelm Wuertz.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ``` ## rsgh - set.seed(1953) r = rsgh(5000, zeta = 1, rho = 0.5, lambda = 1) plot(r, type = "l", col = "steelblue", main = "gh: zeta=1 rho=0.5 lambda=1") ## dsgh - # Plot empirical density and compare with true density: hist(r, n = 50, probability = TRUE, border = "white", col = "steelblue", ylim = c(0, 0.6)) x = seq(-5, 5, length = 501) lines(x, dsgh(x, zeta = 1, rho = 0.5, lambda = 1)) ## psgh - # Plot df and compare with true df: plot(sort(r), (1:5000/5000), main = "Probability", col = "steelblue") lines(x, psgh(x, zeta = 1, rho = 0.5, lambda = 1)) ## qsgh - # Compute Quantiles: round(qsgh(psgh(seq(-5, 5, 1), zeta = 1, rho = 0.5), zeta = 1, rho = 0.5), 4) ```

fBasics documentation built on Nov. 18, 2017, 4:05 a.m.