VGAM (version 0.7-5)

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, ...)

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)