Renext (version 3.1-4)

Hpoints: Plotting positions for exponential return levels

Description

Plotting positions for exponential return level plots.

Usage

Hpoints(n)

Value

Numeric vector of plotting positions with length n.

Arguments

n

Sample size.

Author

Yves Deville

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")