Return Level Plot for GEV Fits
A return level plot is constructed for a GEV-type model.
rlplot.gevff(object, show.plot = TRUE,
probability = c((1:9)/100, (1:9)/10, 0.95, 0.99, 0.995, 0.999),
add.arg = FALSE, xlab = if(log.arg) "Return Period (log-scale)" else
"Return Period", ylab = "Return Level",
main = "Return Level Plot",
pch = par()$pch, pcol.arg = par()$col, pcex = par()$cex,
llty.arg = par()$lty, lcol.arg = par()$col, llwd.arg = par()$lwd,
slty.arg = par()$lty, scol.arg = par()$col, slwd.arg = par()$lwd,
ylim = NULL, log.arg = TRUE, CI = TRUE, epsilon = 1e-05, ...)object |
A VGAM extremes model of the
GEV-type, produced by |
show.plot |
Logical. Plot it? If |
probability |
Numeric vector of probabilities used. |
add.arg |
Logical. Add the plot to an existing plot? |
xlab |
Caption for the x-axis. See |
ylab |
Caption for the y-axis. See |
main |
Title of the plot. See |
pch |
Plotting character. See |
pcol.arg |
Color of the points.
See the |
pcex |
Character expansion of the points.
See the |
llty.arg |
Line type. Line type.
See the |
lcol.arg |
Color of the lines.
See the |
llwd.arg |
Line width.
See the |
slty.arg, scol.arg, slwd.arg |
Correponding arguments for the lines used for the
confidence intervals. Used only if |
ylim |
Limits for the y-axis. Numeric of length 2. |
log.arg |
Logical. If |
CI |
Logical. Add in a 95 percent confidence interval? |
epsilon |
Numeric, close to zero. Used for the finite-difference approximation to the first derivatives with respect to each parameter. If too small, numerical problems will occur. |
... |
Arguments passed into the |
A return level plot plots zp versus
log(yp).
It is linear if the shape parameter xi=0.
If xi<0 then the plot is convex
with asymptotic limit as p approaches zero at
mu-sigma/xi.
And if xi>0 then the plot is concave and has
no finite bound.
Here, G(zp) = 1-p where 0<p<1
(p corresponds to the argument probability)
and G is the cumulative distribution function of the
GEV distribution. The quantity zp is known as the
return level associated with the return period
1/p. For many applications, this means zp
is exceeded by the annual
maximum in any particular year with probability p.
The points in the plot are the actual data.
In the post slot of the object is a list called
rlplot with list components
yp |
|
zp |
values which are used for the y-axis |
lower, upper |
lower and upper confidence limits for the
95 percent confidence intervals evaluated at the values of
|
The confidence intervals are approximate, being based on finite-difference approximations to derivatives.
T. W. Yee
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
gdata <- data.frame(y = rgev(n <- 100, scale = 2, shape = -0.1))
fit <- vglm(y ~ 1, gevff, data = gdata, trace = TRUE)
# Identity link for all parameters:
fit2 <- vglm(y ~ 1, gevff(lshape = identitylink, lscale = identitylink,
iscale = 10), data = gdata, trace = TRUE)
coef(fit2, matrix = TRUE)
## Not run:
par(mfrow = c(1, 2))
rlplot(fit) -> i1
rlplot(fit2, pcol = "darkorange", lcol = "blue", log.arg = FALSE,
scol = "darkgreen", slty = "dashed", las = 1) -> i2
range(i2@post$rlplot$upper - i1@post$rlplot$upper) # Should be near 0
range(i2@post$rlplot$lower - i1@post$rlplot$lower) # Should be near 0
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.