Confidence intervals for the log-normal mean

Abstract

In this paper we conduct a simulation study to evaluate coverage error, interval width and relative bias of four main methods for the construction of confidence intervals of log-normal means: the naive method; Cox's method; a conservative method; and a parametric bootstrap method. The simulation study finds that the naive method is inappropriate, that Cox's method has the smallest coverage error for moderate and large sample sizes, and that the bootstrap method has the smallest coverage error for small sample sizes. In addition, Cox's method produces the smallest interval width among the three appropriate methods. We also apply the four methods to a real data set to contrast the differences.