# Plot L-moment Ratio Diagram (Tau4 and Tau6) 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. ```r 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| ## 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. ## Author(s) W.H. Asquith ## See Also `lmrdia46`, `plotlmrdia` ## Examples ```r 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) ```

plotlmrdia46 function