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Biometrika 1979 66(3):567-575; doi:10.1093/biomet/66.3.567
© 1979 by Biometrika Trust
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Confidence estimation of measures of location in the log normal distribution

ERIK MOHN

Norwegian Computing Center Blindern, Oslo

Based on a random sample from the N({xi}, {sigma}1) distribution, we find confidence bands with level 1 – {alpha} for exp({xi} +b{sigma}1) for all 6. The method is based on a technique discussed by Kanofeky (1968a, b). Using the likelihood ratio confidence region for ({xi}, {sigma}1) (Spjøtvoll, 1972) as starting point we find that the probability that the confidence interval for a particular value of b covers the true value is fairly constant under variation of b, {sigma} and the sample size. This makes it possible to construct confidence intervals with levels approximately equal to a preassigned value. Choosing b = 1/2 we obtain an interval for the expectation of the log normal distribution. It has practically the same expected width as an approximate interval suggested by Cox (Land, 1972). The confidence band obtained by using the confidence region proposed by Mood (1950, p. 228) is compared with the likelihood ratio band and seems to have less favourable statistical properties.

Key Words: Confidence band • Likelihood ratio • Log normal distribution • Measure of location


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