evplot.rfd: Extreme-value plot of a regional frequency distribution

Description

Plots a regional frequency distribution, optionally with error bounds for either the regional growth curve or the quantile function for an individual site.

The graph is an “extreme-value plot”, i.e. the horizontal axis is the quantile of an extreme-value type I (Gumbel) distribution, and the quantile function of that distribution would plot as a straight line.

Usage

# S3 method for rfd
evplot(y, ybounds, npoints=101, add=FALSE, plim,
  xlim=c(-2,5), ylim,
  xlab=expression("Reduced variate,  " * -log(-log(italic(F)))),
  ylab="Quantile", rp.axis=TRUE, type="l", lty=c(1,2), col=c(1,1),
  ...)

Arguments

y: Object of class rfd, containing the specification of a regional frequency distribution.
ybounds: Optional. Object of class rfdbounds (typically created by regquantbounds or sitequantbounds), containing error bounds for quantile estimates for the regional frequency distribution specified by y.
npoints: Number of points to use in drawing the quantile function. The points are equally spaced along the x axis.
add: Logical: if TRUE, add to existing plot.
plim: X axis limits, specified as probabilities.
xlim: X axis limits, specified as values of the Gumbel reduced variate $-\log(-\log(F))$, where $F$ is the nonexceedance probability. Not used if plim is specified.
ylim: Y axis limits.
xlab: X axis label.
ylab: Y axis label.
rp.axis: Logical: whether to draw the “Return period” axis, a secondary horizontal axis.
type: Vector of plot types. The first element is for the quantile function; subsequent elements are for the error bounds, and will be used cyclically until all lines are drawn. Interpreted in the same way as the type plotting parameter, i.e. "l" for lines, "b" for points connected by lines, etc.
lty: Vector of line types. The first element is for the quantile function; subsequent elements are for the error bounds, and will be used cyclically until all lines are drawn.
col: Vector of colors. The first element is for the quantile function; subsequent elements are for the error bounds, and will be used cyclically until all lines are drawn.
...: Additional parameters are passed to the plotting routine.

Author

J. R. M. Hosking jrmhosking@gmail.com

Details

If ybounds is missing, a graph is drawn of the quantile function (regional growth curve) of the distribution specified by y.

If ybounds is present, it may contain error bounds for either a regional growth curve or the quantile function at a single site. This regional growth curve or site quantile function is plotted using arguments type[1], lty[1] and col[1]. Then, in each case, error bounds are added to the plot. The ybounds object typically contains, for several probabilities specified by ybounds$bounds, error bounds corresponding to that probability for several quantiles. For thejth bound probability, the bounds for the various quantiles will be joined by straight lines (so to obtain a smooth curve there should be a lot of quantiles!), using graphics parameters type[j+1], lty[j+1] and col[j+1].

Examples

Run this code

Cascades                        # An object of class "regdata"
rfit <- regfit(Cascades, "gno") # Fit a generalized normal distribution

evplot(rfit)                    # Plot the regional growth curve

# Compute error bounds for quantile estimates.  We will
# (optimistically) generate bounds for a homogeneous region
# with the same frequency distribution as the one fitted to
# the Cascades data.
fval <- seq(.01, .99, by=.01)   # A lot of quantiles
simq <- regsimq(rfit$qfunc, nrec=Cascades$n, nrep=100, f=fval,
  fit=rfit$dist)

# Regional growth curve, and bounds
rbounds <- regquantbounds(simq, rfit)
evplot(rfit, rbounds)

# Quantile function for site 3, and bounds
sbounds <- sitequantbounds(simq, rfit, site=3)
evplot(rfit, sbounds)