evd (version 1.2-3)

rl: A Return Level Plot for an evd Object

Description

A return level plot for an evd object.

Usage

pp(x, ci = TRUE, main = "Quantile Plot", xlab = "Model", 
    ylab = "Empirical", ...)

Arguments

x

An object of class "evd".

ci

Logical; if TRUE (the default), plot simulated 95% confidence intervals.

main

Title of plot.

xlab,ylab

Labels for x and y axes.

...

Other plot parameters.

Details

Let $G$ be the generalized extreme value distribution function, with location, scale and shape parameters $a$, $b$ and $s$ respectively. Let $z_t$ be defined by $G(z_t) = 1 - 1/t$. In common terminology, $z_t$ is the return level associated with the return period $t$.

Let $y_t = -1/\log(1 - 1/t)$. It follows that $$z_t = a + b(y_t^s - 1)/s.$$ When $s = 0$, $z_t$ is defined by continuity, so that $$z_t = a + b\log(y_t).$$ The curve within the return level plot is $z_t$ plotted against $y_t$ on a logarithmic scale, using maximum likelihood estimates of $(a,b,s)$. If the estimator of $s$ is zero, the curve will be linear. For large values of $t$, $y_t$ is approximately equal to $t$.

The points on the plot are $${(-1/\log(p_i), z_i), i = 1,\ldots,m}$$ where $p_1,\ldots,p_m$ are plotting points defined by ppoints, and $z_1,\ldots,z_m$ are the data used in the fitted model, sorted into ascending order. For a good fit the points should lie ``close'' to the curve defined by $(z_t,\log(y_t))$.

For non-stationary models the data are transformed to stationarity. The plot then corresponds to the distribution obtained when all covariates are zero.

See Also

dens, plot.evd, ppoints, pp, qq

Examples

uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2)
M1 <- fgev(uvdata)
rl(M1)