SkewHyperbolicPlots {SkewHyperbolic}

Skew Hyperbolic Student t-Distribution Quantile-Quantile and Percent-Percent Plots

Description

qqskewhyp produces a skew hyperbolic t-distribution Q-Q plot of the values in y, ppskewhyp produces a skew hyperbolic t-distribution P-P (percent-percent) plot or probability plot of the values in y. Graphical parameters may be given as arguments to qqskewhyp and ppskewhyp.

Usage

qqskewhyp(y, mu = 0, delta = 1, beta = 1, nu = 1,
          param = c(mu, delta, beta, nu),
          main = "Skew Hyperbolic Student-t QQ Plot",
          xlab = "Theoretical Quantiles", ylab = "Sample Quantiles",
          plot.it = TRUE, line = TRUE, ...)
ppskewhyp(y, beta = NULL, delta = NULL, mu = NULL, nu = NULL,
          param = c(mu, delta, beta, nu),
          main = "Skew Hyperbolic Student-t P-P Plot",
          xlab = "Uniform Quantiles",
          ylab = "Probability-integral-transformed Data",
          plot.it = TRUE, line = TRUE, ...)

Arguments

y

The sample data.

mu

Location parameter \mu, default is 0.

delta

Scale parameter \delta, default is 1.

beta

Skewness parameter \beta, default is 1.

nu

Shape parameter \nu, default is 1.

param

Specifying the parameters as a vector of the form
c(mu,delta,beta,nu).

main, xlab, ylab

Plot labels.

plot.it

Logical; if plot.it = TRUE the results will be plotted.

line

Logical; if line = TRUE a line is added through the origin with unit slope.

...

Further graphical parameters.

Details

Users may either specify the values of the parameters individually or as a vector. If both forms are specified, then the values specified by the vector param will overwrite the other ones.

Value

For qqskewhyp and ppskewhyp, a list with components:

x

The x coordinates of the points to be plotted.

y

The y coordinates of the points to be plotted.

Author(s)

David Scott [e-mail], Fiona Grimson

References

Aas, K. and Haff, I. H. (2006). The Generalised Hyperbolic Skew Student's t-distribution, Journal of Financial Econometrics, 4, 275–309.

See Also

ppoints, qqplot, dskewhyp

Examples

par(mfrow = c(1,2))
param <- c(0,1,0,10)
y <- rskewhyp(500, param = param)
qqskewhyp(y, param = param, main = "Skew Hyperbolic\n Q-Q Plot")
ppskewhyp(y, param = param, main = "Skew Hyperbolic\n P-P Plot")