lmomsRCmark {lmomco}

Sample L-moments Moments for Right-Tail Censoring by a Marking Variable

Description

Compute the sample L-moments for right-tail censored data set in which censored data values are identified by a marking variable. Extension of left-tail censoring can be made using fliplmoms and the example therein.

Usage

lmomsRCmark(x, rcmark=NULL, nmom=5, flip=NA, flipfactor=1.1)

Arguments

x

A vector of data values.

rcmark

The right-tail censoring (upper) marking variable for unknown threshold: 0 is uncensored, 1 is censored.

nmom

Number of L-moments to return.

flip

Do the data require flipping so that left-censored data can be processed as such. If the flip is a logical and TRUE, then flipfactor \times \mathrm{max}(x) (the maximum of x) is used. If the flip is a numeric, then it is used as the flip.

flipfactor

The value that is greater than 1, which is multiplied on the maximum of x to determine the flip, if the flip is not otherwise provided.

Value

An R list is returned.

lambdas

Vector of the L-moments. First element is \hat{\lambda}^{(0,0)}_1, second element is \hat{\lambda}^{(0,0)}_2, and so on. The returned mean is NOT unflipped.

ratios

Vector of the L-moment ratios. Second element is \hat{\tau}^{(0,0)}, third element is \hat{\tau}^{(0,0)}_3 and so on.

trim

Level of symmetrical trimming used in the computation, which will equal NULL if asymmetrical trimming was used. This is not currently implemented as no one has done the derivations.

leftrim

Level of left-tail trimming used in the computation. This is not currently implemented as no one has done the derivations.

rightrim

Level of right-tail trimming used in the computation. This is not currently implemented as no one has done the derivations.

n

The complete sample size.

n.cen

The number of right-censored data values.

flip

The flip used in the computations for support of left-tail censoring.

source

An attribute identifying the computational source of the L-moments: “lmomsRCmark”.

Author(s)

W.H. Asquith

References

Wang, Dongliang, Hutson, A.D., Miecznikowski, J.C., 2010, L-moment estimation for parametric survival models given censored data: Statistical Methodology, v. 7, no. 6, pp. 655–667.

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

See Also

lmomRCmark, fliplmoms

Examples

# Efron, B., 1988, Logistic regression, survival analysis, and the
# Kaplan-Meier curve: Journal of the American Statistical Association,
# v. 83, no. 402, pp.414--425
# Survival time measured in days for 51 patients with a marking
# variable in the "time,mark" ensemble. If marking variable is 1,
# then the time is right-censored by an unknown censoring threshold.
Efron <-
c(7,0,  34,0,  42,0,  63,0,  64,0,  74,1,  83,0,  84,0,  91,0,
108,0,  112,0,  129,0,  133,0,  133,0,  139,0,  140,0,  140,0,
146,0,  149,0,  154,0,  157,0,  160,0,  160,0,  165,0,  173,0,
176,0,  185,1,  218,0,  225,0,  241,0,  248,0,  273,0,  277,0,
279,1,  297,0,  319,1,  405,0,  417,0,  420,0,  440,0,  523,1,
523,0,  583,0,  594,0,  1101,0,  1116,1,  1146,0,  1226,1,
1349,1,  1412,1, 1417,1);

# Break up the ensembles into to vectors
ix <- seq(1,length(Efron),by=2)
T  <- Efron[ix]
Efron.data <- T;
Efron.rcmark <- Efron[(ix+1)]

lmr.RC <- lmomsRCmark(Efron.data, rcmark=Efron.rcmark)
lmr.ub <- lmoms(Efron.data)
lmr.noRC <- lmomsRCmark(Efron.data)
PP <- pp(Efron.data)
plot(PP, Efron.data, col=(Efron.rcmark+1), ylab="DATA")
lines(PP, qlmomco(PP, lmom2par(lmr.noRC, type="kap")), lwd=3, col=8)
lines(PP, qlmomco(PP, lmom2par(lmr.ub, type="kap")))
lines(PP, qlmomco(PP, lmom2par(lmr.RC, type="kap")), lwd=2, col=2)
legend(0,1000,c("uncensored L-moments by indicator (Kappa distribution)",
                "unbiased L-moments (Kappa)",
           "right-censored L-moments by indicator (Kappa distribution)"),
                lwd=c(3,1,2), col=c(8,1,2))

########
ZF <- 5 # discharge of undetection of streamflow
Q <- c(rep(ZF,8), 116, 34, 56, 78, 909, 12, 56, 45, 560, 300, 2500)
Qc <- Q == ZF; Qc <- as.numeric(Qc)
lmr     <- lmoms(Q)
lmr.cen <- lmomsRCmark(Q, rcmark=Qc, flip=TRUE)
flip <- lmr.cen$flip
fit  <- pargev(lmr);                     fit.cen <- pargev(lmr.cen)
F <- seq(0.001, 0.999, by=0.001)
Qfit     <-        qlmomco(    F, fit    )
Qfit.cen <- flip - qlmomco(1 - F, fit.cen) # remember to reverse qdf
plot(pp(Q),sort(Q), log="y", xlab="NONEXCEED PROB.", ylab="QUANTILE")
lines(F, Qfit);   lines(F, Qfit.cen,col=2)