fliplmoms: Flip L-moments by Flip Attribute in L-moment Vector

Description

This function flips the L-moments by a flip attribute in an L-moment object such as that returned by lmomsRCmark. The function will attempt to identify the L-moment object and lmorph as necessary, but this support is not guaranteed. The flipping process is used to support left-tail censoring using the right-tail censoring alogrithms of the package. The odd order (seq(3,n,by2)) $\lambda_r$ and $\tau_r$ are negated. The mean $\hat\lambda_1$ is computed by subtracting the $\lambda_1$ from the lmom argument from the flip M: $\hat\lambda_1 = M - \lambda_1$ and the $\tau_2$ is subsequently adjusted by the new mean. This function is written to provide a convenient method to re-transform or back flip the L-moments computed by lmomsRCmark. Careful analysis of the example problem listed here should be made.

Usage

fliplmoms(lmom, flip=NULL, checklmom=TRUE)

Arguments

lmom

A L-moment object created by lmomsRCmark or other vectorize L-moment list.

flip

lmomsRCmark provides the flip, but for other vectorized L-moment list support, the flip can be set by this argument.

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 $\tau_3$ inequal

Value

An R list is returned that matches the structure of the lmom argument (unless an lmorph was attempted). The structure is intended to match that coming from lmomsRCmark.

References

Wang, Dongliang, Hutson, A.D., Miecznikowski, J.C., 2010, L-moment estimation for parametric survival models given censored data: Statistical Methodology, preprint

Helsel, D.R., 2005, Nondetects and data analysis---Statistics for censored environmental data: Hoboken, New Jersey, John Wiley, 250 p.

Examples

Run this code

# Create some data with **multiple detection limits**
# This is a left-tail censoring problem--flipping will be required.
fakedat1 <- rnorm(50, mean=16, sd=5);
fake1.left.censor.indicator <- fakedat1 < 14;
fakedat1[fake1.left.censor.indicator]   <- 14;

fakedat2 <- rnorm(50, mean=16, sd=5);
fake2.left.censor.indicator <- fakedat2 < 10;
fakedat2[fake2.left.censor.indicator]   <- 10;

# combine the data sets
fakedat <- c(fakedat1, fakedat2);
fake.left.censor.indicator <- c(fake1.left.censor.indicator,
                                fake2.left.censor.indicator);
ix <- order(fakedat);
fakedat <- fakedat[ix];
fake.left.censor.indicator <- fake.left.censor.indicator[ix];

lmr.usual       <- lmoms(fakedat);
lmr.flipped     <- lmomsRCmark(fakedat, flip=TRUE,
                               rcmark=fake.left.censor.indicator);
lmr.backflipped <- fliplmoms(lmr.flipped); # re-transform
pch <- as.numeric(fake.left.censor.indicator)*15 + 1;
F <- nonexceeds();
plot(pp(fakedat), sort(fakedat), pch=pch,
     xlab="NONEXCEEDANCE PROBABILITY",
     ylab="DATA VALUE");
lines(F, qlmomco(F, parnor(lmr.backflipped)), lwd=2)
lines(F, qlmomco(F, parnor(lmr.usual)), lty=2)
legend(0,20, c("Uncensored", "Left-tail censored"), pch=c(1,16))
# The solid line represented the Normal distribution fit by
# censoring indicator on the multiple left-tail detection limits.


# see example in pwmRC
H <- c(3,4,5,6,6,7,8,8,9,9,9,10,10,11,11,11,13,13,13,13,13,
       17,19,19,25,29,33,42,42,51.9999,52,52,52)
# 51.9999 was really 52, a real (noncensored) data point.
flip <- 100
F <- flip - H # 
RCpwm <- pwmRC(H, threshold=52)
lmorph(pwm2lmom(vec2pwm(RCpwm$Bbetas))) # OUTPUT1 STARTS HERE

LCpwm <- pwmLC(F, threshold=(flip - 52))
LClmr <- pwm2lmom(vec2pwm(LCpwm$Bbetas))
LClmr <- lmorph(LClmr)
#LClmr$flip <- 100; fliplmoms(LClmr) # would also work
fliplmoms(LClmr, flip=flip) # OUTPUT2 STARTS HERE

# The two outputs are the same showing how the flip
# argument works