Lognormal Prediction Limit for the Arithmetic Mean of n future samples
pl.exe (302 KB)

This program computes the 95% lognormal prediction limit for a future mean of n samples based on a historical set of m samples. For example, in ground-water assessment and corrective action monitoring and/or site assessments, we may wish to compute a 95% prediction limit for the arithmetic mean of 10 on-site measurements based on a background sample of 20 measurements obtained from a series of off-site or upgradient monitoring locations (e.g. ground-water monitoring wells). If the data (e.g. arsenic concentrations in ug/L) are normally distributed, then

is the 95% normal upper prediction limit. When the data are lognormally distributed, using the exponential of the above equation computed on the natural log transformed data provides a prediction limit for the median of the n future samples and not the mean. The program, referenced developed in connection with the paper by Bhaumik and Gibbons (2004) in Technometrics (and referenced therein), provides the appropriate lognormal prediction limit for the mean of the n future samples.
"An Upper Prediction Limit for the Arithmetic Mean of a Lognormal Random Variable" by Bhaumik D.K., and Gibbons R.D. (2004) Technometrics, 46, 239-248