tlmrgev: Compute Select TL-moment ratios of the Generalized Extreme...

tlmrgevR Documentation

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


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.


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



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.


Level of trimming of the left-tail of the sample.


Level of trimming of the right-tail of the sample.


Location parameter of the distribution.


Scale parameter of the distribution.


The beginning κ value of the distribution.


The ending κ value of the distribution.


The increment for the seq() between kbeg and kend.


An R list is returned.


A vector of the τ^{(t_1,t_2)}_2 values.


A vector of the τ^{(t_1,t_2)}_3 values.


A vector of the τ^{(t_1,t_2)}_4 values.


A vector of the τ^{(t_1,t_2)}_5 values.


A vector of the τ^{(t_1,t_2)}_6 values.


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


W.H. Asquith

See Also

quagev, theoTLmoms


## 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.