parln3 {lmomco}

Estimate the Parameters of the 3-Parameter Log-Normal Distribution

Description

This function estimates the parameters (\zeta, lower bounds; \mu_{\mathrm{log}}, location; and \sigma_{\mathrm{log}}, scale) of the Log-Normal3 distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments are seen under lmomln3. The function uses algorithms of the Generalized Normal for core computations. Also, if \tau_3 \le 0, then the Log-Normal3 distribution can not be fit, however reversing the data alleviates this problem.

Usage

parln3(lmom, zeta=NULL, checklmom=TRUE, ...)

Arguments

lmom

An L-moment object created by lmoms or vec2lmom.

zeta

Lower bounds, if NULL then solved for.

checklmom

Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \tau_4 and \tau_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.

...

Other arguments to pass.

Details

Let the L-moments by in variable lmr, if the \zeta (lower bounds) is unknown, then the algorithms return the same fit as the Generalized Normal will attain. However, pargno does not have intrinsic control on the lower bounds and parln3 does. The \lambda_1, \lambda_2, and \tau_3 are used in the fitting for pargno and parln3 but only \lambda_1 and \lambda_2 are used when the \zeta is provided as in parln3(lmr, zeta=0). In otherwords, if \zeta is known, then \tau_3 is not used and shaping comes from the choice of \zeta.

Value

An R list is returned.

type

The type of distribution: ln3.

para

The parameters of the distribution.

source

The source of the parameters: “parln3”.

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

See Also

lmomln3, cdfln3, pdfln3, qualn3, pargno

Examples

lmr <- lmoms(rnorm(20))
parln3(lmr)

## Not run: 
# Handling condition of negative L-skew
# Data reversal looks like: Y <- -X, but let us use an example
# on the L-moments themselves.
lmr.pos <- vec2lmom(c(100, 45, -0.1)) # parln3(lmr.pos) fails
lmr.neg <- lmr.pos
lmr.neg$lambdas[1] <- -lmr.neg$lambdas[1]
lmr.neg$ratios[3]  <- -lmr.neg$ratios[3]
F <- nonexceeds()
plot(F, -qualn3(1-F, parln3(lmr.neg)), type="l", lwd=3, col=2) # red line
lines(F, quagno(F, pargno(lmr.pos))) # black line 
## End(Not run)