qqhyperb function

Hyperbolic Quantile-Quantile and Percent-Percent Plots

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

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

Graphical parameters may be given as arguments to qqhyperb, and pphyperb.

qqhyperb(y, mu = 0, delta = 1, alpha = 1, beta = 0,
         param = c(mu, delta, alpha, beta),
         main = "Hyperbolic Q-Q Plot",
         xlab = "Theoretical Quantiles",
         ylab = "Sample Quantiles",
         plot.it = TRUE, line = TRUE, ...)

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

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.
• param: Parameters of the 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.

Returns

For qqhyperb and pphyperb, 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.

References

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

See Also

ppoints, dhyperb, hyperbFit

Examples

par(mfrow = c(1, 2))
param <- c(2, 2, 2, 1.5)
y <- rhyperb(200, param = param)
qqhyperb(y, param = param, line = FALSE)
abline(0, 1, col = 2)
pphyperb(y, param = param)