# lmomsRCmark: Sample L-moments Moments for Right-Tail Censoring by a... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## 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

 1 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{λ}^{(0,0)}_1, second element is \hat{λ}^{(0,0)}_2, and so on. The returned mean is NOT unflipped. ratios Vector of the L-moment ratios. Second element is \hat{τ}^{(0,0)}, third element is \hat{τ}^{(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”.

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.

lmomRCmark, fliplmoms

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 # 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) 

### Example output




lmomco documentation built on March 14, 2020, 5:06 p.m.