efclnp: Nonparametric Confidence Limits for the Exceedance Fraction

In STAND: Statistical Analysis of Non-Detects

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 γ. Default is 0.95
L	L is specified limit for the exceedance fraction; e.g., the occupational exposure limit

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.

Value

A LIST with components:

fnp	nonparametric estimate of exceedance fraction (as percent)
fnp.LCL	is the 100*γ% lower confidence limit for fnp
fnp.UCL	is the 100*γ% upper confidence limit for fnp
L	is specified limit for the exceedance fraction( e.g. OEL)
gam	one-sided confidence level γ. Default is 0.95

Assumptions

All non-detects < L

Note

The estimates of the exceedance fraction and CL's are in percentage units

Author(s)

E. L. Frome

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))

Example output

Loading required package: survival
      fnp   fnp.LCL   fnp.UCL         L     gamma 
1.4285714 0.4894026 3.2391198 0.2000000 0.9500000 
        f     f.LCL     f.UCL         L       gam 
1.0058636 0.5197721 1.8493091 0.2000000 0.9500000 

STAND documentation built on May 2, 2019, 3:39 p.m.