tlmrln3: 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)

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.

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.

Author

W.H. Asquith

Examples

Run this code

if (FALSE) {
  # 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
}