tlmrln3: Compute Select TL-moment ratios of the 3-Parameter Log-Normal...

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

Compute Select TL-moment ratios of the 3-Parameter Log-Normal Distribution

Description

This function computes select TL-moment ratios of the Log-Normal3 distribution for defaults of \zeta = 0 and \mu_\mathrm{log} = 0. 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 \zeta and \mu_\mathrm{log}. If the message

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

occurs then careful adjustment of the shape parameter \sigma_\mathrm{log} 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

tlmrln3(trim=NULL, leftrim=NULL, rightrim=NULL,
        zeta=0, mulog=0, sbeg=0.01, send=3.5, 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.
zeta	Location parameter of the distribution.
mulog	Mean of the logarithms of the distribution.
sbeg	The beginning \sigma_\mathrm{log} value of the distribution.
send	The ending \sigma_\mathrm{log} value of the distribution.
by	The increment for the seq() between sbeg and send.

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

qualn3, theoTLmoms, tlmrgno

Examples

## Not run: 
  # Recalling that generalized Normal and log-Normal3 are
  # the same with the GNO being the more general.

  # Plot and L-moment ratio diagram of Tau3 and Tau4
  # with exclusive focus on the GNO 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,
             nogev=TRUE, nocau=TRUE, noexp=TRUE, nonor=TRUE,
             nogum=TRUE, noray=TRUE, nouni=TRUE)

  LN3 <- tlmrln3(sbeg=.001, mulog=-1)
  lines(LN3$tau3, LN3$tau4) # See how it overplots the GNO
  # for right skewness. So only part of the GNO is covered.

  # Compute the TL-moment ratios for trimming of one
  # value on the left and four on the right.
  J <- tlmrgno(kbeg=-3.5, kend=3.9, leftrim=1, rightrim=4)
  lines(J$tau3, J$tau4, lwd=2, col=2) # RED CURVE

  LN3 <- tlmrln3(, leftrim=1, rightrim=4, sbeg=.001)
  lines(LN3$tau3, LN3$tau4) # See how it again over plots
  # only part of the GNO

## End(Not run)

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