plotlmrdia: Plot L-moment Ratio Diagram (Tau3 and Tau4)

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Plot L-moment Ratio Diagram (Tau3 and Tau4)

Description

Plot the Tau3-Tau4 L-moment ratio diagram of L-skew and L-kurtosis from a Tau3-Tau4 L-moment ratio diagram object returned by lmrdia. This diagram is useful for selecting a distribution to model the data. The application of L-moment diagrams is well documented in the literature. This function is intended to function as a demonstration of L-moment ratio diagram plotting with enough user settings for many practical applications.

Usage

plotlmrdia(lmr=NULL, nopoints=FALSE, nolines=FALSE, nolimits=FALSE,
           noaep4=FALSE, nogev=FALSE, noglo=FALSE,  nogno=FALSE, nogov=FALSE,
           nogpa=FALSE,  nope3=FALSE, nopdq3=FALSE, nowei=TRUE,
           nocau=TRUE,   noexp=FALSE, nonor=FALSE,  nogum=FALSE,
           noray=FALSE, nosla=TRUE, nouni=FALSE,
           xlab="L-skew (Tau3), dimensionless",
           ylab="L-kurtosis (Tau4), dimensionless", add=FALSE, empty=FALSE,
           autolegend=FALSE, xleg=NULL, yleg=NULL, legendcex=0.9,
           ncol=1, text.width=NULL, lwd.cex=1, expand.names=FALSE, ...)

Arguments

lmr	L-moment diagram object from lmrdia, if NULL, then empty is internally set to TRUE.
nopoints	If TRUE then point distributions are not drawn.
nolines	If TRUE then line distributions are not drawn.
nolimits	If TRUE then theoretical limits of L-moments are not drawn.
noaep4	If TRUE then the lower bounds line of Asymmetric Exponential Power distribution is not drawn.
nogev	If TRUE then line of Generalized Extreme Value distribution is not drawn.
noglo	If TRUE then line of Generalized Logistic distribution is not drawn.
nogno	If TRUE then line of Generalized Normal (Log-Normal3) distribution is not drawn.
nogov	If TRUE then line of Govindarajulu distribution is not drawn.
nogpa	If TRUE then line of Generalized Pareto distribution is not drawn.
nope3	If TRUE then line of Pearson Type III distribution is not drawn.
nopdq3	If TRUE then line of Polynomial Density-Quantile3 distribution is not drawn.
nowei	If TRUE then line of the Weibull distribution is not drawn. The Weibull is a reverse of the Generalized Extreme Value. Traditionally in the literature, the Tau3-Tau4 L-moment ratio diagram have usually included the Weibull distribution and therefore the default setting of this argument is to not plot the Weibull.
nocau	If TRUE then point (TL-moment [trim=1]) of the Cauchy distribution is not drawn.
noexp	If TRUE then point of Exponential distribution is not drawn.
nonor	If TRUE then point of Normal distribution is not drawn.
nogum	If TRUE then point of Gumbel distribution is not drawn.
noray	If TRUE then point of Rayleigh distribution is not drawn.
nouni	If TRUE then point of Uniform distribution is not drawn.
nosla	If TRUE then point (TL-moment [trim=1]) of the Slash distribution is not drawn.
xlab	Horizonal axis label passed to xlab of the plot function.
ylab	Vertical axis label passed to ylab of the plot function.
add	A logical to toggle a call to plot to start a new plot, otherwise, just the trajectories are otherwise plotted.
empty	A logical to return before any trajectories are plotted but after the condition of the add has been evaluated.
autolegend	Generate the legend by built-in algorithm.
xleg	X-coordinate of the legend. This argument is checked for being a character versus a numeric. If it is a character, then yleg is not needed and xleg and take on “location may also be specified by setting x to a single keyword” as per the functionality of graphics::legend() itself.
yleg	Y-coordinate of the legend.
legendcex	The cex to pass to graphics::legend().
ncol	The number of columns in which to set the legend items (default is 1, which differs from legend() default of 1).
text.width	Argument of the same name for legend. Setting to 0.1 for ncol set to 2 seems to work pretty well when two columns are desired.
lwd.cex	Expansion factor on the line widths.
expand.names	Expand the distribution names in the legend.
...	Additional arguments passed into plot() and legend() functions..

Note

This function provides hardwired calls to lines and points to produce the diagram. The plot symbology for the shown distributions is summarized here. The Asymmetric Exponential Power and Kappa (four parameter) and Wakeby (five parameter) distributions are not well represented on the diagram as each constitute an area (Kappa) or hyperplane (Wakeby) and not a line (3-parameter distributions) or a point (2-parameter distributions). However, the Kappa demarks the area bounded by the Generalized Logistic (glo) on the top and the theoretical L-moment limits on the bottom. The Asymmetric Exponential Power demarks its own unique lower boundary and extends up in the \tau_4 direction to \tau_4 = 1. However, parameter estimation with L-moments has lost considerable accuracy for \tau_4 that large (see Asquith, 2014).

GRAPHIC TYPE	GRAPHIC NATURE
L-moment Limits	line width 2 and color a medium-dark grey
Asymmetric Exponential Power (4-p)	line width 1, line type 4 (dot), and color red
Generalized Extreme Value (GEV)	line width 1, line type 1 (solid), and color darkred
Generalized Logistic	line width 1 and color green
Generalized Normal	line width 1, line type 2 (dash), and color blue
Govindarajulu	line width 1, line type 2 (dash), and color 6 (magenta)
Generalized Pareto	line width 1, line type 1 (solid), and color blue
Pearson Type III	line width 1, line type 1 (solid), and color 6 (purple)
Polynomial Density-Quantile3	line width 1.3, line type 2 (dash), and color darkgreen
Weibull (reversed GEV)	line width 1, line type 1 (solid), and color darkorange
Exponential	symbol 16 (filled circle) and color red
Normal	symbol 15 (filled square) and color red
Gumbel	symbol 17 (filled triangle) and color red)
Rayleigh	symbol 18 (filled diamond) and color red
Uniform	symbol 12 (square and a plus sign) and color red
Cauchy	symbol 13 (circle with over lapping \times) and color turquoise4
Slash	symbol 10 (cicle containing +) and color turquoise4

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

Asquith, W.H., 2014, Parameter estimation for the 4-parameter asymmetric exponential power distribution by the method of L-moments using R: Computational Statistics and Data Analysis, v. 71, pp. 955–970.

Hosking, J.R.M., 1986, The theory of probability weighted moments: Research Report RC12210, IBM Research Division, Yorkton Heights, N.Y.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis–An approach based on L-moments: Cambridge University Press.

Vogel, R.M., and Fennessey, N.M., 1993, L moment diagrams should replace product moment diagrams: Water Resources Research, v. 29, no. 6, pp. 1745–1752.

See Also

lmrdia, plotlmrdia46, plotradarlmr

Examples

plotlmrdia(lmrdia()) # simplest of all uses

## Not run: 
# A more complex example follows: for a given mean, L-scale, L-skew, and L-kurtosis,
# use sample size of 30, use 500 simulations, set L-moments, fit the Kappa distribution
T3 <- 0.34; T4 <- 0.21; n <- 30; nsim <- 500
lmr <- vec2lmom(c(10000, 7500, T3, T4)); kap <- parkap(lmr)

# create vectors for storing simulated L-skew (t3) and L-kurtosis (t4)
t3 <- t4 <- vector(mode="numeric")

# perform nsim simulations by randomly drawing from the Kappa distribution
# and compute the L-moments in sim.lmr and store the t3 and t4 of each sample
for(i in 1:nsim) {
  sim.lmr <- lmoms(rlmomco(n, kap))
  t3[i] <- sim.lmr$ratios[3]; t4[i] <- sim.lmr$ratios[4]
}

# plot the diagram and "zoom" by manually setting the axis limits
plotlmrdia(xlim=c(-0.1, 0.5), ylim=c(-0.1, 0.4), las=1, empty=TRUE)

# Follow up by plotting the {t3, t4} values and the mean of the values
points(t3, t4, pch=21, bg="white", lwd=0.8) # plot each simulation

# plot crossing dashed lines at true values of L-skew and L-kurtosis
abline(v=T3, col="salmon4", lty=2, lwd=3) # Theoretical values for the
abline(h=T4, col="salmon4", lty=2, lwd=3) # distribution as fit

points(mean(t3), mean(t4), pch=16, cex=3) # mean of simulations and
# should plot reasonably close to the salmon4-colored crossing lines

# plot the trajectories of the distributions
plotlmrdia(lmrdia(), add=TRUE, nopoints=TRUE, inset=0.01,
           autolegend=TRUE, xleg="topleft", lwd.cex=1.5) # 
## End(Not run)

wasquith/lmomco documentation built on May 6, 2024, 1:43 a.m.