pwmLC: Sample Probability-Weighted Moments for Left-Tail Censoring

Description

Compute the sample Probability-Weighted Moments (PWMs) for left-tail censored data set---that is a data set censored from below. The censoring threshold is denoted as $T$.

Usage

pwmLC(x, threshold=NULL, nmom=5, sort=TRUE)

Arguments

A vector of data values.

threshold

The left-tail censoring (lower) threshold.

nmom

Number of PWMs to return.

sort

Does the data need sorting? Note that convention is the have a $\beta'_0$, but this is placed in the first index i=1 of the betas vector.

Value

An R list is returned.
AprimebetasThe A'-type PWMs. These should be same as pwm() returns if there is no censoring. Note that convention is the have a $\beta_0$, but this is placed in the first index i=1 of the betas vector.
BprimebetasThe B'-type PWMs. These should be NA if there is no censoring. Note that convention is the have a $\beta_0$, but this is placed in the first index i=1 of the betas vector.
sourceSource of the PWMs: pwmLC
thresholdThe upper censoring threshold.
zetaThe right censoring fraction: numbelowthreshold/samplesize
numbelowthresholdNumber of data points equal to or above the threshold.
observedsizeNumber of real data points in the sample (above the threshold).
samplesizeNumber of actual sample values.

Details

There is some ambiguity if the threshold also numerically equals valid data in the data set. In the data for the examples below, which are taken from elsewhere, there are real observations at the censoring level. One can see how a hack is made to marginally decrease or increase the data or the threshold for the computations. This is needed because the code uses sapply(x, function(v) aleftbrace if(v >= T) return(T); return(v) arightbrace ) to reset the data vector x. The aleftbrace or arightbrace is to be interpreted as meaning a brace as used in a programming syntax. By operating on the data in this fashion one can toy with various levels of the threshold for experimental purposes; this seemed a more natural way for general implementation. The code sets $n$=length(x) and $m$=n - length(x[x == T]), which also seems natural. The $\beta^A_r$ are computed by dispatching to pwm.

References

Zafirakou-Koulouris, A., Vogel, R.M., Craig, S.M., and Habermeier, J., 1998, L-moment diagrams for censored observations: Water Resources Research, v. 34, no. 5, pp. 1241-1249.

Examples

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