Description Usage Arguments Note Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 | ```
plotlmrdia(lmr=NULL, 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", add=FALSE, empty=FALSE,
autolegend=FALSE, xleg=NULL, yleg=NULL, ...)
``` |

`lmr` |
L-moment diagram object from |

`nopoints` |
If |

`nolines` |
If |

`nolimits` |
If |

`noaep4` |
If |

`nogev` |
If |

`noglo` |
If |

`nogno` |
If |

`nogov` |
If |

`nogpa` |
If |

`nope3` |
If |

`nocau` |
If |

`noexp` |
If |

`nonor` |
If |

`nogum` |
If |

`noray` |
If |

`nouni` |
If |

`nosla` |
If |

`xlab` |
Horizonal axis label passed to |

`ylab` |
Vertical axis label passed to |

`add` |
A logical to toggle a call to |

`empty` |
A logical to return before any trajectories are plotted but after the condition of the |

`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 |

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

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.

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 | ```
plotlmrdia(lmrdia()) # simplest of all uses
## Not run:
# A more complex example follows.
# For a given mean, L-scale, L-skew, and L-kurtosis, let us use a sample size
# of 30 and using 500 simulations, set the L-moments in lmr and fit the Kappa.
T3 <- 0.34; T4 <- 0.21; n <- 30; nsim <- 500
lmr <- vec2lmom(c(10000,7500,T3,T4)); kap <- parkap(lmr)
# Next, create vectors for storing simulated L-skew (t3) and L-kurtosis (t4)
t3 <- t4 <- vector(mode = "numeric")
# 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 of each sample.
for(i in 1:nsim) {
sim.lmr <- lmoms(rlmomco(n,kap))
t3[i] <- sim.lmr$ratios[3]; t4[i] <- sim.lmr$ratios[4]
}
# Next, plot the diagram with a legend at a specified location, and "zoom"
# into the diagram by manually setting the axis limits.
plotlmrdia(lmrdia(), autolegend=TRUE, xleg=0.1, yleg=.41,
xlim=c(-.1,.5), ylim=c(-.1,.4), nopoints=TRUE, empty=TRUE)
# Follow up by plotting the {t3,t4} values and the mean of these.
points(t3,t4)
points(mean(t3),mean(t4),pch=16,cex=3)
# Now plot the trajectories of the distributions.
plotlmrdia(lmrdia(), add=TRUE)
# Finally, plot crossing dashed lines at true 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)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.