Tail Plot Line

Description

Adds skew hyperbolic t-distribution line to a tail plot

Usage

skewhypTailPlotLine(x, mu = 0, delta = 1, beta = 1, nu = 1,
                    param = c(mu,delta,beta,nu),
                    side = c("right", "left"), ...)

Arguments

Details

The function tailPlot from DistributionUtils can be used to draw 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.

skewhypTailPlotLine adds the line derived from the given skew hyperbolic t-distribution to an already drawn tail plot.

Value

Returns NULL invisibly.

Author(s)

David Scott d.scott@auckland.ac.nz

References

Aas, Kjersti and Hob<c3><a6>k 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.

See Also

tailPlot and skewhypFit.

Examples

### Draw tail plot of some data
param <- c(0,1,1,10)
x <- rskewhyp(200, param = param)
tailPlot(x)
### Add skew hyperbolic t-distribution line
skewhypTailPlotLine(x, param = param)
### Parameters from fit may look better
paramFit <- skewhypFit(x, plots = FALSE)$param
tailPlot(x)
skewhypTailPlotLine(x, param = param)
skewhypTailPlotLine(x, param = paramFit, col = "steelblue")

### Left tail example
tailPlot(x, side = "l")
### Add skew hyperbolic t-distribution line
skewhypTailPlotLine(x, param = paramFit, side = "l")
### Log scale on both axes
tailPlot(x, side = "r", log = "xy")
### Add skew hyperbolic t-distribution line
skewhypTailPlotLine(x, param = paramFit, side = "r")

Results