plotlmrdia46: Plot L-moment Ratio Diagram (Tau4 and Tau6)
In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

plotlmrdia46

R Documentation

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, 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.
`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 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.

Examples

plotlmrdia46(lmrdia46(), nogld_byt5opt=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)

lmomco documentation built on May 29, 2024, 10:06 a.m.