lmomco (version 1.4.3)

tlmrwei: Compute Select TL-moment ratios of the Weibull Distribution

Description

This function computes select TL-moment ratios of the Weibull Value distribution for $\xi = 0$ and $\alpha = 1$ without a loss of generality. This function can be useful for plotting the trajectory of the distribution on TL-moment ratio diagrams of $\tau_3$ and $\tau_4$.

If the message Error in integrate(XofF, 0, 1) : the integral is probably divergent occurs then careful adjustment of the shape parameter $\delta$ 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 L-moments.

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

Usage

tlmrwei(trim=NULL, leftrim=NULL, rightrim=NULL,
        dbeg=-10, dend=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.

dbeg

The beginning $\delta$ value of the distribution.

dend

The ending $\delta$ value of the distribution.

by

The increment for the seq() between dbeg and dend.

Value

• An R list is returned.
• tau3
  A vector of the $\tau^{(t_1,t_2)}_3$ values.
• tau4
  A vector of the $\tau^{(t_1,t_2)}_4$ values.

See Also

quawei, theoTLmoms

Examples

# Plot and L-moment ratio diagram of Tau3 and Tau4
  # with exclusive focus on the WEI 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 <- tlmrwei(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 <- tlmrwei(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.
# Following up, let us plot the two quantile functions
  LM  <- vec2par(c(0,1,-0.99), type='wei', paracheck=FALSE)
  TLM <- vec2par(c(0,1,-4.99), type='wei', 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 WEI.