STAND (version 2.0)

efraction.exact: Exceedance Fraction and Exact Confidence Limits

Description

Calculate estimate of the exceedance fraction $FL = Pr [X > L]$ and exact confidence limits for random sample from normal/lognormal distribution. This function should only be used for complete samples.

Usage

efraction.exact(x, gam = 0.95, L=NA ,logx=TRUE,wpnt=FALSE)

Arguments

x

vector of data values

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

logx

If TRUE, sample is from lognormal, else normal. Default is TRUE

wpnt

if TRUE, show warning from pnt. Default is $FALSE$

Value

A LIST with components:

f

estimate of exceedance fraction for lognormal distribution as %

fe.LCL

100*$\gamma$% exact lower confidence limit % units

fe.UCL

100*$\gamma$% exact upper confidence limit % units

L

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

gam

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

Logx

If TRUE, sample is from lognormal, else normal. Default is TRUE

Details

The exceedance fraction represent the proportion of the X's that exceed a given limit Lp. The null hypothesis of interest is $Ho: F \ge Fo = 1-p$; i.e., Fo is the maximum proportion of the population that can exceed the limit Lp. The null hypothesis is rejected if the $100 \gamma\%$ UCL for FL is less than Fo , indicating that the exposure profile is acceptable. The type I error rate for this test is less than or equal to $\alpha = 1 - \gamma$.

References

Johnson, N. L. and B. L. Welch (1940), "Application of the Non-Central t-Distribution," Biometrika, 31(3/4), 362-389.

Lyles, R. H. and L. L. Kupper (1996), "On strategies for comparing occupational exposure data to limits," American Industrial Hygiene Association Journal. 57:6-15.

Frome, E. L. and Wambach, P. F. (2005), "Statistical Methods and Software for the Analysis of Occupational Exposure Data with Non-Detectable Values," ORNL/TM-2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf

Ignacio, J. S. and W. H. Bullock (2006), A Strategy for Assesing and Managing Occupational Exposures, Third Edition, AIHA Press, Fairfax, VA.

Mulhausen, J. R. and J. Damiano (1998), A Strategy for Assessing and Managing Occupational Exposures, Second Edition, AIHA Press, Fairfax, VA.

See Also

Help files for efraction.ml,efclnp, percentile.exact, efraction.exact, aihand

Examples

# calculate exceedance fraction and exact CLs for Example data
# Appendix  Mulhausen and Damiano(1998) Ignacion and Bullock (2006
data(aihand)
x <- aihand$x ;  det <- rep(1,length(x))
aiha<-data.frame(x,det) #  complete data
unlist(efraction.exact(x,gam=0.95,L=5) ) #  exact CLs
unlist(efraction.ml(aiha,gam=0.95,L=5))  #  ML CLs
unlist(efclnp(aiha,L=5))                 #  nonparametric CLs