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

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 \xi = 0 and \beta = 1. This function can be useful for plotting the trajectory of the distribution on TL-moment ratio diagrams of \tau^{(t_1,t_2)}_2, \tau^{(t_1,t_2)}_3, \tau^{(t_1,t_2)}_4, \tau^{(t_1,t_2)}_5, and \tau^{(t_1,t_2)}_6. In reality, \tau^{(t_1,t_2)}_2 is dependent on the values for \xi and \alpha. If the message

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

occurs then careful adjustment of the shape parameter \beta 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 \alpha value of the distribution.
aend	The ending \alpha 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 \tau^{(t_1,t_2)}_2 values.
tau3	A vector of the \tau^{(t_1,t_2)}_3 values.
tau4	A vector of the \tau^{(t_1,t_2)}_4 values.
tau5	A vector of the \tau^{(t_1,t_2)}_5 values.
tau6	A vector of the \tau^{(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

See Also

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 May 29, 2024, 10:06 a.m.