STAND (version 2.0)

efclnp: Nonparametric Confidence Limits for the Exceedance Fraction

Description

When the distribution function for the X's is not specified a nonparametric approach can be used to estimate the exceedance fraction $FL = Pr [X > L]$ the proportion of measurements that exceed the limit L.

Usage

efclnp(dd,gam = 0.95,L)

Arguments

dd

An n by 2 matrix or data frame with x (exposure) variable in column 1, and det = 0 for non-detect or 1 for detect in column 2

gam

one-sided confidence level $\gamma$. Default is 0.95

L

L is specified limit for the exceedance fraction; e.g., the occupational exposure limit

Value

A LIST with components:

fnp

nonparametric estimate of exceedance fraction (as percent)

fnp.LCL

is the 100*$\gamma$% lower confidence limit for fnp

fnp.UCL

is the 100*$\gamma$% upper confidence limit for fnp

L

is specified limit for the exceedance fraction( e.g. OEL)

gam

one-sided confidence level $\gamma$. Default is 0.95

Assumptions

All non-detects < L

Details

Given a random sample of size n the number y of nonconforming observations (i.e., y = number of X's that exceed the limit L) is described using the binomial distribution. The point estimate of FL is $fnp = y / n$ and confidence limits are obtained using the method of Clopper and Pearson (1934) (Hahn and Meeker, 1991) and the R documentation for base R function binom.test.

References

Clopper, C. J. and E. S. Pearson (1934), "The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial," Biometrika, 26, 404-413.

Hahn, G. J. and W. Q. Meeker (1991), Statistical Intervals, John Wiley and Sons, New York.

See Also

efraction.ml

Examples

#   calculate nonparametric estimate 
#   for Example 2 in ORNLTM2005 
data(beTWA)
unlist(efclnp(beTWA,L=0.2))
# calculate ML estimates of exceedance fraction and CLs 
unlist(efraction.ml(beTWA,L=0.2))