Sample L-moments Moments for Right-Tail Censoring by a Marking Variable
Sample L-moments Moments for Right-Tail Censoring by a Marking Variable
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.
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×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.
Returns
An list is returned.
lambdas: Vector of the L-moments. First element is λ^1(0,0), second element is λ^2(0,0), and so on. The returned mean is NOT unflipped.
ratios: Vector of the L-moment ratios. Second element is τ^(0,0), third element is τ^3(0,0) 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 .
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.
Author(s)
W.H. Asquith
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 vectorsix <- 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 streamflowQ <- 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 qdfplot(pp(Q),sort(Q), log="y", xlab="NONEXCEED PROB.", ylab="QUANTILE")lines(F, Qfit); lines(F, Qfit.cen,col=2)