A Comparison of Tests on the Mean of a Logarithmico-Normal Distribution with Known Variance

Abstract

Three test procedures are considered for testing an hypothesis on the mean of a logarithmico-normal distribution with known variance. The first is a normal theory test applied to the logarithms of the original data; the second is a normal theory test applied to the original data; and the third is a test based on the Neyman-Pearson Lemma. The operating characteristics of these tests are developed and some asymptotic properties obtained. It is found that the three procedures give quite different results unless the mean under the null hypothesis is large relative to the standard deviation.