lmomco (version 2.0.1)

parln3: Estimate the Parameters of the 3-Parameter Log-Normal Distribution

Description

This function estimates the parameters of the Log-Normal3 distribution given the L-moments of the data in an L-moment object such as that returned by lmom.ub. The relation between distribution parameters and L-moments is 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

A L-moment object created by lmom.ub or pwm2lmom.

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 $\tau_3$ inequ

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.

References

NEED

See Also

lmom.ub, lmomln3, cdfln3, qualn3

Examples

lmr <- lmom.ub(rnorm(20))
parln3(lmr)

# 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