R: Tail Plot Functions

tailPlot {DistributionUtils} | R Documentation

## Tail Plot Functions

### Description

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`

### Usage

    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, (> 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.

### Value

Returns `NULL` invisibly.

### Author(s)

David Scott d.scott@auckland.ac.nz

### References

Aas, Kjersti and Hobæk 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 Würtz, 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

### 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)

[Package DistributionUtils version 0.6-0 Index]