lmrd {lmom}R Documentation

L-moment ratio diagram

Description

Draws an L-moment ratio diagram.

Usage

lmrd(x, y, distributions = "GLO GEV GPA GNO PE3", twopar,
     xlim, ylim, pch=3, col, lty, lwd=1,
     legend.lmrd = TRUE, xlegend, ylegend,
     xlab = expression(italic(L) * "-skewness"),
     ylab = expression(italic(L) * "-kurtosis"), ...)

Arguments

x Numeric vector of L-skewness values.
Alternatively, if the y argument is omitted, x can be a vector of L-moment ratios, as returned for example by function samlmu. In this case the third and fourth elements of x are taken to be L-skewness and L-kurtosis respectively and are plotted.
y Numeric vector of L-kurtosis values.
distributions Indicates the three-parameter distributions whose L-skewness–L-kurtosis relations are to be plotted as lines on the diagram. The following distributions are recognized:
GLO generalized logistic
GEV generalized extreme-value
GPA generalized Pareto
GNO generalized normal
PE3 Pearson type III
WAK.LB lower bound of L-kurtosis for given L-skewness,
for the Wakeby distribution.
ALL.LB lower bound of L-kurtosis for given L-skewness,
for all distributions.

The argument should be either a character vector each of whose elements is one of the above abbreviations or a character string containing one or more of the abbreviations separated by blanks. The specified L-skewness–L-kurtosis curves will be plotted.
If no three-parameter distributions are to be plotted, specify distributions to be FALSE or the empty string, "".
twopar Two-parameter distributions whose (L-skewness, L-kurtosis) values are to be plotted as points on the diagram. The following distributions are recognized:
E or EXP exponential
G or GUM Gumbel
L or LOG logistic
N or NOR normal
U or UNI uniform

The argument should be either a character vector each of whose elements is one of the above abbreviations or a character string containing one or more of the abbreviations separated by blanks. L-skewness–L-kurtosis points for the specified distributions will be plotted and given one-character labels.
The default is to plot the two-parameter distributions that are special cases of the three-parameter distributions specified in the distributions parameter. Thus for example if distributions="GPA PE3", the default for twopar is "EXP NOR UNI": NOR is a special case of PE3, UNI of GPA, EXP of both GPA and PE3.
If no two-parameter distributions are to be plotted, specify twopar to be FALSE or the empty string, "".
xlim x axis limits. Default: c(0, 0.6), expanded if necessary to cover the range of the data.
ylim y axis limits. Default: c(0, 0.4), expanded if necessary to cover the range of the data.
pch Plotting character to be used for the plotted (L-skewness, L-kurtosis) points.
col Vector specifying the colors to be used for the lines on the plot. For the default values, see the description of the lty argument below.
lty Vector specifying the line types to be used for the lines on the plot.
By default, colors and line types are matched to the distributions given in the distributions parameter, as follows:
GLO color "blue", solid line
GEV color "green", solid line
GPA color "red", solid line
GNO color "black", solid line
PE3 color "cyan", solid line
WAK.LB color "red", dashed line
ALL.LB color "black", dashed line
lwd Vector specifying the line widths to be used for the lines on the plot.
legend.lmrd Controls whether a legend, identifying the L-skewness–L-kurtosis relations of the three-parameter distributions, is plotted. Not used if distributions=FALSE.
xlegend x coordinate of the upper left corner of the legend. Default: the minimum x value. Not used if distributions=FALSE or legend.lmrd=FALSE.
ylegend y coordinate of the upper left corner of the legend. Default: the maximum y value. Not used if distributions=FALSE or legend.lmrd=FALSE.
xlab X axis label.
ylab Y axis label.
... Additional arguments are passed to the matplot function that draws the axis box and the lines for three-parameter distributions.

Details

lmrd calls a sequence of graphics functions: matplot for the axis box and the curves for three-parameter distributions; points for the points for two-parameter distributions and text for their labels; legend for the legend; and points for the (x,y) data points.

Note that additional parameters (...) are passed only to matplot, and cannot be used to change the color of plotted points. To do so, follow lmrd by an additional call to the points function, e.g. follow lmrd(t3, t4) by points(t3, t4, col="red").

Author(s)

J. R. M. Hosking hosking@watson.ibm.com

Examples

data(airquality)
lmrd(samlmu(airquality$Ozone))
# Tweaking a few graphics parameters makes the graph look better
# (in the author's opinion)
lmrd(samlmu(airquality$Ozone), xaxs="i", yaxs="i", las=1)

# An example that illustrates the sampling variability of L-moments
#
# Generate 50 random samples of size 30 from the Gumbel distribution
# - stored in the rows of matrix mm
mm <- matrix(quagum(runif(1500)), nrow=50)
#
# Compute the first four sample L-moments of each sample
# - stored in the rows of matrix aa
aa <- apply(mm, 1, samlmu)
#
# Plot the L-skewness and L-kurtosis values on an L-moment ratio
# diagram that also shows (only) the population L-moment ratios
# of the Gumbel distribution
lmrd(aa[3,], aa[4,], dist="", twopar="G")

[Package lmom version 1.2 Index]