Compute Select TL-moment ratios of the Pearson Type III

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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

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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

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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

See Also

quape3, theoTLmoms

Examples

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## 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)

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