QQ-Plot for Any Distribution

Create a QQ-plot for a variable of any distribution. The assumed underlying distribution can be defined as a function of f(p), including all required parameters. Confidence bands are provided by default.

PlotQQ(x, qdist=qnorm, main = NULL, xlab = NULL, ylab = NULL, datax = FALSE, add = FALSE,
       args.qqline = NULL, conf.level = 0.95, args.cband = NULL, ...)

Arguments

x

the data sample

qdist

the quantile function of the assumed distribution. Can either be given as simple function name or defined as own function using the required arguments. Default is qnorm(). See examples.

main

the main title for the plot. This will be "Q-Q-Plot" by default

xlab

the xlab for the plot

ylab

the ylab for the plot

datax

logical. Should data values be on the x-axis? Default is FALSE.

add

logical specifying if the points should be added to an already existing plot; defaults to FALSE.

args.qqline

arguments for the qqline. This will be estimated as a line through the 25% and 75% quantiles by default, which is the same procedure as qqline() does for normal distribution (instead of set it to abline(a = 0, b = 1)). The quantiles can however be overwritten by setting the argument probs to some user defined values. Also the method for calculating the quantiles can be defined (default is 7, see quantile). The line defaults are set to col = par("fg"), lwd = par("lwd") and lty = par("lty"). No line will be plotted if args.qqline is set to NA.

conf.level

confidence level for the confidence interval. Set this to NA, if no confidence band should be plotted. Default is 0.95. The confidence intervals are calculated pointwise method based on a Kolmogorov-Smirnov distribution.

args.cband

list of arguments for the confidence band, such as color or border (see DrawBand).

...

the dots are passed to the plot function.

Details

The function generates a sequence of points between 0 and 1 and transforms those into quantiles by means of the defined assumed distribution.

Note

The code is inspired by the tip 10.22 "Creating other Quantile-Quantile plots" from R Cookbook and based on R-Core code from the function qqline. The calculation of confidence bands are rewritten based on an algorithm published in the package BoutrosLab.plotting.general.

References

Teetor, P. (2011) R Cookbook. O'Reilly, pp. 254-255.

Author

Andri Signorell <andri@signorell.net>, Ying Wu <Ying.Wu@stevens.edu>

See also

qqnorm, qqline, qqplot

Examples

y <- rexp(100, 1/10)
PlotQQ(y, function(p) qexp(p, rate=1/10))


w <- rweibull(100, shape=2)
PlotQQ(w, qdist = function(p) qweibull(p, shape=4))


z <- rchisq(100, df=5)
PlotQQ(z, function(p) qchisq(p, df=5),
       args.qqline=list(col=2, probs=c(0.1, 0.6)),
       main=expression("Q-Q plot for" ~~ {chi^2}[nu == 3]))
abline(0,1)

# add 5 random sets
for(i in 1:5){
  z <- rchisq(100, df=5)
  PlotQQ(z, function(p) qchisq(p, df=5), add=TRUE, args.qqline = NA,
         col="grey", lty="dotted")
}