# plotlmrdia: Plot L-moment Ratio Diagram In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

Plot the L-moment ratio diagram of L-skew and L-kurtosis from an 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.

## Usage

 1 2 3 4 5 6 7 plotlmrdia(lmr, nopoints=FALSE, nolines=FALSE, nolimits=FALSE, noaep4=FALSE, nogev=FALSE, noglo=FALSE, nogpa=FALSE, nope3=FALSE, nogno=FALSE, nogov=FALSE, nocau=TRUE, noexp=FALSE, nonor=FALSE, nogum=FALSE, noray=FALSE, nosla=TRUE, nouni=FALSE, xlab="L-SKEW", ylab="L-KURTOSIS", autolegend=FALSE, xleg=NULL, yleg=NULL, ...) 

## Arguments

 lmr L-moment diagram object from lmrdia. 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 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. nocau If TRUE then point (limiting, 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 (limiting, 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. autolegend Generate the legend by built-in algorithm. xleg X-coordinate of the legend. yleg Y-coordinate of the legend. ... Additional arguments passed onto the plot function.

## 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 τ_4 direction to τ_4 = 1. However, parameter estimation with L-moments has lost considerable accuracy for τ_4 that large (see Asquith, 2014).

 GRAPHIC TYPE GRAPHIC NATURE L-moment Limits line width 2 and color 8 (grey) Asymmetric Exponential Power (4-p) line width 1, line type 4 (dot), and color 2 (red) Generalized Extreme Value line width 1, line type 2 (dash), and color 2 (red) Generalized Logistic line width 1 and color 3 (green) Generalized Normal line width 1, line type 2 (dash), and color 4 (blue) Govindarajulu line width 1, line type 2 (dash), and color 6 (purple) Generalized Pareto line width 1 and color 4 (blue) Pearson Type III line width 1 and color 6 (purple) Exponential symbol 16 (filled circle) and color 2 (red) Normal symbol 15 (filled square) and color 2 (red) Gumbel symbol 17 (filled triangle) and color 2 (red) Rayleigh symbol 18 (filled diamond) and color 2 (red) Uniform symbol 12 (square and a plus sign) and color 2 (red) Cauchy symbol 13 (circle with over lapping \times) and color 3 (green) Slash symbol 10 (cicle containing +) and color 3 (green)

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.

lmrdia, plotradarlmr

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 plotlmrdia(lmrdia()) # simplest of all uses ## Not run: # A more complex example follows. # For a given mean, L-scale, L-skew and L-kurtosis, a sample size # of 30 and using 50 simulations, set the L-moments in lmr and fit # a Kappa distribution T3 <- 0.34; T4 <- 0.21; n <- 30; nsim <- 50; lmr <- vec2lmom(c(10000,7500,T3,T4)); kap <- parkap(lmr) # Next, create vectors for storage of simulated L-skew (t3) # and L-kurtosis (t4) t3 <- vector(mode = "numeric"); t4 <- t3; # Next, perform nsim simulations by randomly drawing from the Kappa # distribution and compute the L-moments in sim.lmr and store the # t3 and t4 values of each simulated sample. for(i in 1:nsim) { sim.lmr <- lmoms(rlmomco(n,kap)) t3[i] <- sim.lmr$ratios[3]; t4[i] <- sim.lmr$ratios[4] } # Finally, plot the diagram with a legend at a specified location, # and "zoom" into the diagram by setting the axis limits. plotlmrdia(lmrdia(), autolegend=TRUE, xleg=0.1, yleg=.41, xlim=c(-.1,.5), ylim=c(-.1,.4), nopoints=TRUE) # Follow up with plotting of the t3,t4 values and the mean of these. points(t3,t4) points(mean(t3),mean(t4),pch=16,cex=3) # A complete the example by plotting crossing dashed lines at the # population values of L-skew and L-kurtosis lines(c(T3,T3),c(-1,1),col=8, lty=2) lines(c(-1,1),c(T4,T4),col=8, lty=2) # ## End(Not run) 

### Example output




lmomco documentation built on March 18, 2018, 1:45 p.m.