UKFE (version 2.0.0)

ERPlot: Extreme rank plot

Description

A plot to inspect the distribution of ordered data

Usage

ERPlot(x, dist = "GenLog", main = NULL, Pars = NULL, GF = NULL, ERType = 1)

Value

The extreme rank plot as described in the details

Arguments

x

numeric vector. A sample for inspection

dist

a choice of distribution. The choices are "GenLog" (the default), "GEV", "Kappa3,"Gumbel", and "GenPareto"

main

a character string to change the default title, which is the distribution choice.

Pars

a vector of parameters for the distribution. In the order of location, scale, & shape (ignoring the latter if Gumbel). If left null the parameters are estimated from x.

GF

a vector of length growth curve parameters, in the order of; Lcv, LSkew and Median (ignoring the LSkew if Gumbel).

ERType

Either 1, 2. If it is the default 1 then ranks are plotted on the x axis and percentage difference of modelled from observed is plotted on the y axis.

Author

Anthony Hammond

Details

By default this plot compares the percentage difference of simulated results with observed for each rank of the data. Another option (see ERType argument) compares the simulated flows for each rank of the sample with the observed of the same rank. For both plots 500 simulated samples are used. With the second option for each rank they are plotted and the mean of these is highlighted in red. There is a line of perfect fit so you can see how much this "cloud" of simulation differs from the observed. By default the parameters of the distribution for comparison with the sample are estimated from the sample. However, the pars argument can be used to compare the distribution with parameters estimated separately. Similarly the growth factor (GF) parameters, linear coefficient of variation (Lcv) & linear skewness (LSkew) with the median can be entered. In this way the pooling estimated distribution can be compared to the sample. This ERplot is an updated version of that described in Hammond, A. (2019). Proposal of the 'extreme rank plot' for extreme value analysis: with an emphasis on flood frequency studies. Hydrology Research, 50 (6), 1495-1507.

Examples

# Get an AMAX sample and plot
if (FALSE) {
am_27083 <- GetAM(27083)
ERPlot(am_27083$Flow)
}

# Assume pooled estimates of Lcv and LSkew of 0.23, 0.17, and a QMED of 12.
# Use these inputs for the GF argument and change the title
if (FALSE) {
ERPlot(am_27083$Flow, main = "Site 27083 pooled comparison", GF = c(0.23, 0.17, 12))
}