Renext (version 3.0-0)

Hpoints: Plotting positions for exponential return levels

Description

Plotting positions for exponential return level plots.

Usage

Hpoints(n)

Arguments

n

Sample size.

Value

• Numeric vector of plotting positions with length n.

encoding

UTF-8

Details

The plotting positions are numeric values to use as the abscissae corresponding to the order statistics in an exponential return level plot. They range from 1 to about $\log n$. They can be related to the plotting positions given by ppoints.

The returned vector $\mathbf{H}$ has elements $$H_{i} = \frac{1}{n} + \frac{1}{n-1} + \dots + \frac{1}{n + 1 -i}$$ for $1 \leq i \leq n$. This is the expectation of the $i$-th order statistic for a sample of the standard exponential distribution, see e.g. chap. 4 of Embrechts et al.

References

Embrechts P., Klüppelberg C. and Mikosch T. (1997) Modelling Extremal Events for Insurance and Finance. Springer.

See Also

ppoints.

Examples

n <- 30
set.seed(1234)
x <- rGPD(n, shape = 0.2)
plot(exp(Hpoints(n)), sort(x), log = "x",
     main = "Basic return level plot")