Sample size determination and the effect of censoring when estimating the arithmetic mean of a lognormal distribution

Abstract

This article presents several formulas to approximate the required sample size to estimate the arithmetic mean of a lognormal distribution with desired accuracy and confidence under and without the presence of type I censoring to the left. We present tables of exact sample sizes which are based on Land's exact confidence interval of the lognormal mean.

In the case of non censoring, Box-Cox transformations were used to derive formulae for approximating these exact sample sizes and new formulae, adjusting the classic central limit approach, were derived. Each of these formulas as well as other existing formulas (the classical central limit approach.

Keywords:

• confidence interval width
• sample size determination
• Box-Cox transformation
• uniformly most accurate unbiased invariant confidence interval
• bias correction
• maximum likelihood estimator