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 March 13, 2020, 9:09 a.m.