lmomco (version 2.2.5)

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)

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.

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)