efraction.exact {STAND}

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

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.

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

Note

(fe.LCL, fe.UCL) is an approximate 100(2\gamma -1) percent confidence interval for F. The R function uniroot is used to find the noncentrality parameter of noncentral t distribution to calculate CL's for U = (L - \mu) / \sigma where F = pnorm(U). In some versions of R this may cause a warning message. See R bug report RP 9171 full precision was not achieved in 'pnt'. This warning message may occur in uniroot calls to pt and does not effect the precision of the final result

Author(s)

E. L. Frome

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