Alternatively, if argument y is omitted, x can be an object
that contains both L-skewness and L-kurtosis values.
It can be a vector with elements named
"t_3" and "t_4" (or "tau_3" and "tau_4"),
a matrix or data frame with columns named
"t_3" and "t_4" (or "tau_3" and "tau_4"),
or an object of class "regdata" (as defined in package lmomRFA).
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 distribution identifiers are recognized, in upper or lower case:
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 distribution identifiers are recognized, in upper or lower case:
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
argument distributions. 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.
cex
Symbol size for plotted points, like graphics parameter cex.
col
Vector specifying the colors. If it is of length 1
and x is present, it will be used for the plotted points.
Otherwise it will be used for the lines on the plot.
For the default colors for the lines, see the description
of argument lty 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 argument distributions, as follows:
GLO
blue, solid line
GEV
green, solid line
GPA
red, solid line
GNO
black, solid line
PE3
cyan, solid line
WAK.LB
red, dashed line
ALL.LB
black, dashed line
The green and cyan colors are less bright than the standard
"green" and "cyan"; they are defined to be
"#00C000" and "#00E0E0", respectively.
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.
Either logical, indicating whether a legend is to be drawn,
or a list specifying arguments to the legend function.
Default arguments include bty="n", which must be overridden
if a legend box is to be drawn; other arguments set by default are
x, y, legend, col, lty, and lwd.
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 the only graphics parameters passed to points
are col (if of length 1), cex, and pch.
If more complex features are required, such as different colors for
different points, follow lmrd by an additional call to points,
e.g. follow lmrd(t3, t4) by points(t3, t4, col=c("red", "green")).
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(t(aa), dist="", twopar="G", col="red")