plotlmrdia46: Plot L-moment Ratio Diagram (Tau4 and Tau6)

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

Plot L-moment Ratio Diagram (Tau4 and Tau6)

Description

Plot the Tau4-Tau6 L-moment ratio diagram showing trajectories of \tau_4 and \tau_6 for strictly symmetrical distributions from a Tau4-Tau6 L-moment ratio diagram object returned by lmrdia46. This diagram is useful for selecting among symmetrical distributions to model the data. This function is intended to function as a demonstration of Tau4-Tau6 L-moment ratio diagram plotting with enough user settings for many practical applications.

Usage

plotlmrdia46(lmr=NULL, nopoints=FALSE, nolines=FALSE,
             noaep4=FALSE,  nogld_byt5opt=TRUE, nopdq4=FALSE,  nost3=FALSE,
             nosymgdd=TRUE, nosymstable=FALSE,  notukey=FALSE,
             nocau=TRUE,    nonor=FALSE, nosla=TRUE, trucate.tau4.to.gtzero=TRUE,
             xlab="L-kurtosis (Tau4), dimensionless",
             ylab="Sixth L-moment ratio (Tau6), 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 lmrdia46, 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.
noaep4	If TRUE then the Symmetric Exponential Power distribution is not drawn.
nogld_byt5opt	If TRUE then line of Generalized Lambda distribution through it solution optimization on \tau_5 = 0 is not drawn.
nopdq4	If TRUE then line of Polynomial Density-Quantile4 distribution is not drawn.
nost3	If TRUE then line of Student 3t distribution is not drawn.
nosymgdd	If TRUE then line of a symmetrical Gamma Difference distribution is not drawn.
nosymstable	If TRUE then line of Symmetric Stable distribution is not drawn.
notukey	If TRUE then line of Tukey Lambda distribution is not drawn.
nocau	If TRUE then point of Cauchy distribution (trim=1 L-moments) is not drawn.
nonor	If TRUE then point of Normal distribution is not drawn.
nosla	If TRUE then point of Slash distribution (trim=1 L-moments) is not drawn.
trucate.tau4.to.gtzero	Truncate the distributions that can extend to negative \tau_4 to zero. This is a reasonable default and prevents line drawing to the left into a clipping region for easier handling of post processing of a graphic in vector editing software.
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 the 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.

GRAPHIC TYPE	GRAPHIC NATURE
Symmetric Exponential Power	line width 1, line type 4 (dot), and color red
Generalized Lambda	line width 1, line type 1 (solid), and color purple
Polynomial Density-Quantile4	line width 1, line type 1 (solid), and color darkgreen
Student t	line width 1, line type 1 (solid), and color blue
Symmetric Gamma Difference	line width 2, line type 1 (solid), and color a darkorange2
Symmetric Stable	line width 2, line type 1 (solid), and color a medium-dark grey
Tukey Lambda (1-p)	line width 1, line type 2 (dash), and color purple
Normal	symbol 15 (filled square) 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., 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.

See Also

lmrdia46, plotlmrdia

Examples

plotlmrdia46(lmrdia46(), nogld_byt5opt=FALSE, nosymgdd=FALSE,
             autolegend=TRUE, xleg="topleft")

## Not run: 
# A more complex example follows: for a given mean, L-scale, L-skew = 0 (symmetry), and
# L-kurtosis, use sample size of 30, use 500 simulations, set L-moments,
# fit the Asymmetric Exponential Power4 distribution, which is symmetrical when the
# L-skew is zero and thus the distribution is the Exponential Power.
T3  <- 0; T4 <- 0.21; n <- 30; nsim <- 500
lmr <- vec2lmom(c(10000, 7500, T3, T4, 0)); aep4 <- paraep4(lmr)
T6  <- theoLmoms(aep4, nmom=6)$ratios[6]

# create vectors for storing simulated L-kurtosis (t4) and Tau6 (t6)
t4 <- t6 <- vector(mode="numeric")

# perform nsim simulations by randomly drawing from the AEP4 distribution
# and compute the L-moments in sim.lmr and store the t4 and t6 of each sample
for(i in 1:nsim) {
  sim.lmr <- lmoms(rlmomco(n, aep4), nmom=6)
  t4[i] <- sim.lmr$ratios[4]; t6[i] <- sim.lmr$ratios[6]
}

# plot the diagram and "zoom" by manually setting the axis limits
plotlmrdia46(xlim=c(-0.05, 0.5), ylim=c(-0.1, 0.35), las=1, empty=TRUE)

# follow up by plotting the {t3, t4} values and the mean of the values
points(t4, t6, cex=0.8, 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=T4, col="salmon4", lty=2, lwd=3) # Theoretical values for the
abline(h=T6, col="salmon4", lty=2, lwd=3) # distribution as fit

points(mean(t4), mean(t6), pch=16, cex=3) # mean of simulations and
# should plot reasonably close to the salmon4-colored crossing lines

# plot the trajectories of the distributions
plotlmrdia46(lmrdia46(), add=TRUE, nopoints=TRUE, inset=0.01,
             autolegend=TRUE, xleg="topleft", lwd.cex=1.5) # 
## End(Not run)

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.