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# Technometrics Volume 46 , Issue 2 , 2004


# An Upper Prediction Limit for the Arithmetic Mean of a Lognormal Random Variable PreviewDownload full text Access options DOI: 10.1198/004017004000000284 Dulal Kumar Bhaumik a & Robert David Gibbons a pages 239-248 Publishing models and article dates explained • Published online: 01 Jan 2012 Article Views: 31 Article usage statistics combine cumulative total P DF downloads and full-text HTML views from publicat ion date (but no earlier than 25 Jun 2011, launch date of this website) to 05 Nov 2014. Articl e views are only counted from this site. Although these data are updated every 24 hours, there may be a 48-hour delay before the most recent numbers a re available. Alert me
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# Abstract In this article we construct an upper prediction li mit for the arithmetic mean of a future sample froma lognormal distribution. First, we present three approximate distributions for the total of th e future sample and compare them to the exact distr ibution. Then we use the exact and approximate distributions to construct the desired prediction limit. We study confidence levels for th e different methods via simulation. We illustrate our results with an example and show viasimulation that the desired confidence level is at tained for only one of these methods. We also show that the usual approach to this problem based on logarithmic transformation leads to a prediction limit for the median, which can dramatically underestimate the prediction limit for the mean.
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### KEY WORDS

• Characteristic function , • Edgeworth expansion , • Environmental statistics , • Gram–charlier type A series , • Lognormal , • Prediction limit
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• Published online: 01 Jan 2012 Click to increase image size 

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### Author affiliations

• aCenter for Health Statistics, Departments of Biost atistics and Psychiatry, University of Illinois, Ch icago, IL 60612 

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