lmomco (version 1.7.3)

plotlmrdia: Plot L-moment Ratio Diagram

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 diagram plotting. It is expected that users will roll their own version of this function for their own specific purposes.

Usage

plotlmrdia(lmr, nopoints=FALSE, nolines=FALSE, nolimits=FALSE,
           noaep4=FALSE, nogev=FALSE, noglo=FALSE, nogpa=FALSE,
           nope3=FALSE,  nogno=FALSE, nocau=FALSE, noexp=FALSE,
           nonor=FALSE,  nogum=FALSE, noray=FALSE, 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-Normal) 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) 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.

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.

References

Asquith, W.H., 1998, Depth-duration frequency of precipitation for Texas: U.S. Geological Survey Water-Resources Investigations Report 98-4044, 107 p.

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, vol. 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, vol. 29, no. 6, pp. 1745--1752.

See Also

lmrdia

Examples

plotlmrdia(lmrdia())

# 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)