GeneralizedHyperbolicPlots: Generalized Hyperbolic Quantile-Quantile and Percent-Percent Plots

Description

qqghyp produces a generalized hyperbolic Q-Q plot of the values in y.

ppghyp produces a generalized hyperbolic P-P (percent-percent) or probability plot of the values in y.

Graphical parameters may be given as arguments to qqghyp, and ppghyp.

Usage

qqghyp(y, mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
       param = c(mu, delta, alpha, beta, lambda),
       main = "Generalized Hyperbolic Q-Q Plot",
       xlab = "Theoretical Quantiles",
       ylab = "Sample Quantiles",
       plot.it = TRUE, line = TRUE, ...)
ppghyp(y, mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
       param = c(mu, delta, alpha, beta, lambda),
       main = "Generalized Hyperbolic P-P Plot",
       xlab = "Uniform Quantiles",
       ylab = "Probability-integral-transformed Data",
       plot.it = TRUE, line = TRUE, ...)

Value

For qqghyp and ppghyp, a list with components:

x: The x coordinates of the points that are to be plotted.
y: The y coordinates of the points that are to be plotted.

Arguments

y: The data sample.
mu: \(\mu\) is the location parameter. By default this is set to 0.
delta: \(\delta\) is the scale parameter of the distribution. A default value of 1 has been set.
alpha: \(\alpha\) is the tail parameter, with a default value of 1.
beta: \(\beta\) is the skewness parameter, by default this is 0.
lambda: \(\lambda\) is the shape parameter and dictates the shape that the distribution shall take. Default value is 1.
param: Parameters of the generalized hyperbolic distribution.
xlab, ylab, main: Plot labels.
plot.it: Logical. Should the result be plotted?
line: Add line through origin with unit slope.
...: Further graphical parameters.

References

Wilk, M. B. and Gnanadesikan, R. (1968) Probability plotting methods for the analysis of data. Biometrika. 55, 1--17.

Examples

Run this code

par(mfrow = c(1, 2))
y <- rghyp(200, param = c(2, 2, 2, 1, 2))
qqghyp(y, param = c(2, 2, 2, 1, 2), line = FALSE)
abline(0, 1, col = 2)
ppghyp(y, param = c(2, 2, 2, 1, 2))