lmomco (version 1.4.3)

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 a 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 L-moments.

The function uses numerical integration of the quantile function of the distribution through the theoTLmoms function.

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.

See Also

qualn3, theoTLmoms

Examples

# 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