pwmLC {lmomco}

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

x

A vector of data values.

threshold

The left-tail censoring (lower) threshold.

nmom

Number of PWMs to return.

sort

Do 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.

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) { if(v >= T) return(T); return(v) } )

to reset the data vector x. 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.

Value

An R list is returned.

Aprimebetas

The 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.

Bprimebetas

The 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.

source

Source of the PWMs: “pwmLC”.

threshold

The upper censoring threshold.

zeta

The left censoring fraction: numbelowthreshold/samplesize.

numbelowthreshold

Number of data points equal to or above the threshold.

observedsize

Number of real data points in the sample (above the threshold).

samplesize

Number of actual sample values.

Author(s)

W.H. Asquith

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.

See Also

lmoms, pwm2lmom, pwm, pwmRC

Examples

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