tlmrgpa: Compute Select TL-moment ratios of the Generalized Pareto

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Compute Select TL-moment ratios of the Generalized Pareto

Description

This function computes select TL-moment ratios of the Generalized Pareto distribution for defaults of \xi = 0 and \alpha = 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 \kappa 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.

Usage

tlmrgpa(trim=NULL, leftrim=NULL, rightrim=NULL,
        xi=0, alpha=1, kbeg=-.99, kend=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.
xi	Location parameter of the distribution.
alpha	Scale parameter of the distribution.
kbeg	The beginning \kappa value of the distribution.
kend	The ending \kappa value of the distribution.
by	The increment for the seq() between kbeg and kend.

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

quagpa, theoTLmoms

Examples

## Not run: 
tlmrgpa(leftrim=7, rightrim=2, xi=0, alpha=31)
tlmrgpa(leftrim=7, rightrim=2, xi=143, alpha=98) # another slow example

## End(Not run)
## Not run: 
  # Plot and L-moment ratio diagram of Tau3 and Tau4
  # with exclusive focus on the GPA distribution.
  plotlmrdia(lmrdia(), autolegend=TRUE, xleg=-.1, yleg=.6,
             xlim=c(-.8, .7), ylim=c(-.1, .8),
             nolimits=TRUE, nogev=TRUE, noglo=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 k > -1.
  J <- tlmrgpa(kbeg=-3.2, kend=50, by=.05, leftrim=1, rightrim=4)
  lines(J$tau3, J$tau4, lwd=2, col=2) # RED CURVE
  # Notice the gap in the curve near tau3 = 0.1

  # Compute the TL-moment ratios for trimming of four
  # values on the left and one on the right.
  J <- tlmrgpa(kbeg=-1.6, kend=8, leftrim=4, rightrim=1)
  lines(J$tau3, J$tau4, lwd=2, col=3) # 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='gpa', paracheck=FALSE)
  TLM <- vec2par(c(0,1,3.00), type='gpa', paracheck=FALSE)
  F <- nonexceeds()
  plot(qnorm(F),  quagpa(F, LM), type="l")
  lines(qnorm(F), quagpa(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 GPA.

## End(Not run)

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.