tailPlot function

Tail Plot Functions

Create a left or right tail plot of a data set using tailPlot. Add a line for any distribution with parameters given by an argument named param, using tailPlotLine. Add normal, $t$, or gamma distribution lines to the plot using normTailPlotLine, tTailPlotLine, or gammaTailPlotLine

tailPlot(x, log = "y", side = c("right", "left"), main = NULL,
         xlab = NULL, ylab = NULL, ...)
tailPlotLine(x, distrFn, param = NULL, side = c("right", "left"), ...)
normTailPlotLine(x, mean = 0, sd = 1, side = c("right", "left"), ...)
tTailPlotLine(x, df = Inf, side = c("right", "left"), ...)
gammaTailPlotLine(x, shape = 1, rate = 1, scale = 1/rate,
                  side = c("right", "left"), ...)

Arguments

• x: A vector of values for which the tail plot is to be drawn.
• log: A character string which contains "x" if the x-axis is to be logarithmic, "y" if the y-axis is to be logarithmic and "xy" or "yx" if both axes are to be logarithmic.
• side: Character. "right" (the default) for a tail plot of the right-hand tail, "left" for a tail plot of the left-hand tail.
• main: A main title for the plot.
• xlab: A label for the x axis, defaults to NULL.
• ylab: A label for the y axis, defaults to NULL.
• distrFn: Character. The name of the distribution function to be to be added to the tail plot.
• param: Vector specifying the parameters of the distribution, defaults to NULL.
• mean: The mean of the normal distribution.
• sd: The standard deviation of the normal distribution. Must be positive.
• df: The degrees of freedom of the $t$-distribution, (c("$>\n$", "$0$"), may be non-integer). Defaults to Inf, corresponding to the standard normal distribution.
• shape: The shape parameter of the gamma distribution. Must be positive.
• scale: The scale parameter of the gamma distribution. Must be strictly positive, scale strictly.
• rate: The rate parameter of the gamma distribution. An alternative way to specify the scale.
• ...: Other graphical parameters (see par.

Details

tailPlot draws either a left-hand or right-hand tail plot of the data x. See for example Resnick (2007), p.105. The left-hand tail plot plots the empirical distribution of the data against the order statistics, for order statistic values below the median. The right-hand tail plot plots one minus the empirical distribution of the data against the order statistics, for order statistic values above the median. The default is for the y-axis to be plotted on a log scale.

tailPlotLine adds a line for the specified distribution to an already drawn tail plot. The distribution can be any distribution which has default parameters, but if parameters need to be supplied the distribution must have an argument param which specifies the parameters. This is the case for all distributions in the form recommended in Scott et al (2009) and includes distributions from the packages GeneralizedHyperbolic, SkewHyperbolic, VarianceGamma and NormalLaplace (which is on R-Forge).

normTailPlotLine,tTailPlotLine and gammaTailPlotLine add the corresponding line derived respectively from the given normal, $t$, or gamma distribution to an already drawn tail plot.

Returns

Returns NULL invisibly.

References

Aas, Kjersti and Haff, Ingrid (2006) The generalised hyperbolic skew Student's $t$-distribution. Journal of Financial Econometrics, 4 , 275--309.

Resnick, S. (2007) Heavy-Tail Phenomena, New York: Springer.

Scott, David J. and , Diethelm and Dong, Christine (2009) Software for Distributions in R. UseR: The R User Conference 2009 https://www.r-project.org/conferences/useR-2009/slides/Scott+Wuertz+Dong.pdf

Author(s)

David Scott d.scott@auckland.ac.nz

Examples

### Draw tail plot of some data
x <- rnorm(100, 1, 2)
tailPlot(x)
### Add normal distribution line
normTailPlotLine(x, mean = 1, sd = 2)
### Add t distribution line
tTailPlotLine(x, df = 5, lty = 2)
### Use fitted values
normTailPlotLine(x, mean = mean(x), sd = sd(x), lty = 3)

### Gamma distribution
x <- rgamma(100, shape = 1, scale = 1)
tailPlot(x)
### Add gamma distribution line
gammaTailPlotLine(x, shape = 1, scale = 1)
### Left tail example
tailPlot(x, side = "l")
### Add gamma distribution line
gammaTailPlotLine(x, shape = 1, scale = 1, side = "l")
### Log scale on both axes
tailPlot(x, side = "l", log = "xy")
### Add gamma distribution line
gammaTailPlotLine(x, shape = 1, scale = 1, side = "l")

### Add line from a standard distribution with default parameters
x <- rlnorm(100)
tailPlot(x)
tailPlotLine(x, distrFn = "lnorm")

### Add line from a distribution with 'param' argument
require(VarianceGamma)
param <- c(0,0.5,0,0.5)
x <- rvg(100, param = param)
tailPlot(x)
tailPlotLine(x, distrFn = "vg", param = param)