An Evaluation of Approximate Confidence Interval Estimation Methods for Lognormal Means

Approximate confidence limits for EX, where X is lognormal (μ, σ2), are compared with corresponding exact limits obtained by an optimal method, for various sample sizes and values of the usual sufficient statistic. The approximatemethods examinedare “transformation methods” in which a confidence interval for E(log X) is transformed so as to approximately cover EX, and “direct methods” based on approximate distributions for estimates of EX or of some function of EX. The degree of agreement with the exact method, for the approximate methods examined, appears to be best when 2, the usual unbiased estimate of the variance of log X, is small and the number of degrees of freedom for 2 is large. As 2 increases, however, this agreement becomes less satisfactory, to the extent that, with one exception, the approximate methods examined appear to be of little use unless 2 is small, even for large samples. The exception, a direct method based on an estimate of log (EX), appears to be suitable as a computationally simple large-sample alternative to the exact method.