# tlmrpe3: Compute Select TL-moment ratios of the Pearson Type III In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 tlmrpe3 R Documentation

## Compute Select TL-moment ratios of the Pearson Type III

### Description

This function computes select TL-moment ratios of the Pearson Type III distribution for defaults of ξ = 0 and β = 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 β 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. The function uses numerical integration of the quantile function of the distribution through the `theoTLmoms` function.

### Usage

```tlmrpe3(trim=NULL, leftrim=NULL, rightrim=NULL,
xi=0, beta=1, abeg=-.99, aend=0.99, 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. `beta` Scale parameter of the distribution. `abeg` The beginning α value of the distribution. `aend` The ending α value of the distribution. `by` The increment for the `seq()` between `abeg` and `aend`.

### 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

`quape3`, `theoTLmoms`

### Examples

```## Not run:
tlmrpe3(leftrim=2, rightrim=4, xi=0, beta=2)
tlmrpe3(leftrim=2, rightrim=4, xi=100, beta=20) # another slow example
# Plot and L-moment ratio diagram of Tau3 and Tau4
# with exclusive focus on the PE3 distribution.
plotlmrdia(lmrdia(), autolegend=TRUE, xleg=-.1, yleg=.6,
xlim=c(-.8, .7), ylim=c(-.1, .8),
nolimits=TRUE, nogev=TRUE, nogpa=TRUE, noglo=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 alpha parameter space from
# -1 < a < -1 to something larger based on manual
# adjustments until blue curve encompassed the plot.
J <- tlmrpe3(abeg=-15, aend=6, leftrim=1, rightrim=4)
lines(J\$tau3, J\$tau4, lwd=2, col=2) # RED CURVE

# Compute the TL-moment ratios for trimming of four
# values on the left and one on the right.
J <- tlmrpe3(abeg=-6, aend=10, leftrim=4, rightrim=1)
lines(J\$tau3, J\$tau4, lwd=2, col=4) # BLUE CURVE

# The abeg and aend 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='pe3', paracheck=FALSE)
TLM <- vec2par(c(0,1,3.00), type='pe3', paracheck=FALSE)
F <- nonexceeds()
plot(qnorm(F),  quape3(F, LM), type="l")
lines(qnorm(F), quape3(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 PE3.

## End(Not run)
```

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