Bias in log-transformed frequency distributions

Estimates of the parameters of frequency distributions are often derived from the logarithms of a series of measured data rather than from the original series itself. This is common practice, for example, in estimating flood frequencies from measured streamflow data, extreme wave frequencies from wave height data, as well as in many other contexts. This procedure leads to biased estimates of the moments and quantiles of the frequency distribution in arithmetic space. This bias is the result of the non-linear inverse transformation process. The case of the two parameter lognormal distribution is examined in detail and analytical expressions for the bias are derived. The bias introduced by the logarithmic transformation is dependent on the sample size and the population parameters. The derived analytical expressions for bias agree with the results of a series of Monte Carlo simulations.