# 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

 `1` ```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

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.

`efraction.ml`

## Examples

 ```1 2 3 4 5 6``` ```# 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.