VGAM (version 0.8-2)

meplot: Mean Excess Plot

Description

Mean excess plot (also known as a mean residual life plot), a diagnostic plot for the generalized Pareto distribution (GPD).

Usage

meplot(object, ...)
meplot.default(y, main="Mean Excess Plot",
    xlab="Threshold", ylab="Mean Excess", lty=c(2,1:2),
    conf=0.95, col=c("blue","black","blue"), type="l", ...)
meplot.vlm(object, ...)

Arguments

y

A numerical vector. NAs etc. are not allowed.

main

Character. Overall title for the plot.

xlab

Character. Title for the x axis.

ylab

Character. Title for the y axis.

lty

Line type. The second value is for the mean excess value, the first and third values are for the envelope surrounding the confidence interval.

conf

Confidence level. The default results in approximate 95 percent confidence intervals for each mean excess value.

col

Colour of the three lines.

type

Type of plot. The default means lines are joined between the mean excesses and also the upper and lower limits of the confidence intervals.

object

An object that inherits class "vlm", usually of class vglm-class or vgam-class.

...

Graphical argument passed into plot. See par for an exhaustive list. The arguments xlim and ylim are particularl

Value

• A list is returned invisibly with the following components.
• threshold
  The x axis values.
• meanExcess
  The y axis values. Each value is a sample mean minus a value $u$.

Details

If $Y$ has a GPD with scale parameter $\sigma$ and shape parameter $\xi<1$, and="" if="" $y="">0$, then $$E(Y-u|Y>u) = \frac{\sigma+\xi u}{1-\xi}.$$ It is a linear function in $u$, the threshold. Note that $Y-u$ is called the excess and values of $Y$ greater than $u$ are called exceedences. The empirical versions used by these functions is to use sample means to estimate the left hand side of the equation. Values of $u$ in the plot are the values of $y$ itself. If the plot is roughly a straight line then the GPD is a good fit; this plot can be used to select an appropriate threshold value. See gpd for more details. If the plot is flat then the data may be exponential, and if it is curved then it may be Weibull or gamma.

The function meplot is generic, and meplot.default and meplot.vlm are some methods functions for mean excess plots.

References

Davison, A. C. and Smith, R. L. (1990) Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society, Series B, Methodological, 52, 393--442.

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

See Also

gpd.

Examples

meplot(runif(500), las=1) -> i
names(i)