# skewhypTailPlotLine: Tail Plot Line In SkewHyperbolic: The Skew Hyperbolic Student t-Distribution

## Description

Adds skew hyperbolic t-distribution line to a tail plot

## Usage

 ```1 2 3``` ```skewhypTailPlotLine(x, mu = 0, delta = 1, beta = 1, nu = 1, param = c(mu,delta,beta,nu), side = c("right", "left"), ...) ```

## Arguments

 `x` A vector of values for which the tail plot has been drawn. `side` Character. `"right"` (the default) if the tail plot is of the right-hand tail, `"left"` if the tail plot is of the left-hand tail. `mu` Location parameter mu, default is 0. `delta` Scale parameter delta, default is 1. `beta` Skewness parameter beta, default is 1. `nu` Shape parameter nu, default is 1. `param` Specifying the parameters as a vector of the form `c(mu,delta,beta,nu)`. `...` Other graphical parameters (see `par`.

## 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 [email protected]

## References

Aas, Kjersti and Hob<e6>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.

`tailPlot` and `skewhypFit`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```### Draw tail plot of some data tailPlot <- DistributionUtils :: tailPlot ## for convenience below 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") ```