# tlmrgev: Compute Select TL-moment ratios of the Generalized Extreme... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 tlmrgev R Documentation

## Compute Select TL-moment ratios of the Generalized Extreme Value Distribution

### Description

This function computes select TL-moment ratios of the Generalized Extreme Value distribution for defaults of ξ = 0 and α = 1. This function can be useful for plotting the trajectory of the distribution on TL-moment ratio diagrams of τ^{(t_1,t_2)}_2, τ^{(t_1,t_2)}_3, τ^{(t_1,t_2)}_4, τ^{(t_1,t_2)}_5, and τ^{(t_1,t_2)}_6. In reality, τ^{(t_1,t_2)}_2 is dependent on the values for ξ and α. If the message

`Error in integrate(XofF, 0, 1) : the integral is probably divergent`

occurs then careful adjustment of the shape parameter κ parameter range is very likely required. Remember that TL-moments with nonzero trimming permit computation of TL-moments into parameter ranges beyond those recognized for the usual (untrimmed) L-moments.

### Usage

```tlmrgev(trim=NULL, leftrim=NULL, rightrim=NULL,
xi=0, alpha=1, kbeg=-.99, kend=10, by=.1)
```

### Arguments

 `trim` Level of symmetrical trimming to use in the computations. Although `NULL` in the argument list, the default is 0—the usual L-moment ratios are returned. `leftrim` Level of trimming of the left-tail of the sample. `rightrim` Level of trimming of the right-tail of the sample. `xi` Location parameter of the distribution. `alpha` Scale parameter of the distribution. `kbeg` The beginning κ value of the distribution. `kend` The ending κ value of the distribution. `by` The increment for the `seq()` between `kbeg` and `kend`.

### Value

An R `list` is returned.

 `tau2` A vector of the τ^{(t_1,t_2)}_2 values. `tau3` A vector of the τ^{(t_1,t_2)}_3 values. `tau4` A vector of the τ^{(t_1,t_2)}_4 values. `tau5` A vector of the τ^{(t_1,t_2)}_5 values. `tau6` A vector of the τ^{(t_1,t_2)}_6 values.

### Note

The function uses numerical integration of the quantile function of the distribution through the `theoTLmoms` function.

### Author(s)

W.H. Asquith

`quagev`, `theoTLmoms`

### Examples

```## Not run:
tlmrgev(leftrim=12, rightrim=1, xi=0,   alpha=2 )
tlmrgev(leftrim=12, rightrim=1, xi=100, alpha=20) # another slow example

## End(Not run)
## Not run:
# Plot and L-moment ratio diagram of Tau3 and Tau4
# with exclusive focus on the GEV distribution.
plotlmrdia(lmrdia(), autolegend=TRUE, xleg=-.1, yleg=.6,
xlim=c(-.8, .7), ylim=c(-.1, .8),
nolimits=TRUE, noglo=TRUE, nogpa=TRUE, nope3=TRUE,
nogno=TRUE, nocau=TRUE, noexp=TRUE, nonor=TRUE,
nogum=TRUE, noray=TRUE, nouni=TRUE)

# Compute the TL-moment ratios for trimming of one
# value on the left and four on the right. Notice the
# expansion of the kappa parameter space from > -1 to
# something near -5.
J <- tlmrgev(kbeg=-4.99, leftrim=1, rightrim=4)
lines(J\$tau3, J\$tau4, lwd=2, col=3) # BLUE CURVE

# Compute the TL-moment ratios for trimming of four
# values on the left and one on the right.
J <- tlmrgev(kbeg=-1.99, leftrim=4, rightrim=1)
lines(J\$tau3, J\$tau4, lwd=2, col=4) # GREEN CURVE

# The kbeg and kend can be manually changed to see how
# the resultant curve expands or contracts on the
# extent of the L-moment ratio diagram.

## End(Not run)
## Not run:
# Following up, let us plot the two quantile functions
LM  <- vec2par(c(0,1,-0.99), type='gev', paracheck=FALSE)
TLM <- vec2par(c(0,1,-4.99), type='gev', paracheck=FALSE)
F <- nonexceeds()
plot(qnorm(F),  quagev(F, LM), type="l")
lines(qnorm(F), quagev(F, TLM, paracheck=FALSE), col=2)
# Notice how the TLM parameterization runs off towards
# infinity much much earlier than the conventional
# near limits of the GEV.

## End(Not run)
```

lmomco documentation built on Aug. 27, 2022, 1:06 a.m.