The quality of mean and variance estimates for normal and lognormal data when the underlying distribution is misspecified

Theoretical and simulation results are employed to evaluate mean and variance estimates for normal data when a lognormal distribution is assumed and for lognormal data when a normal distribution is assumed. Misspecifying the distribution leads to the use of suboptimal estimation methods. However, the results show that the suboptimal methods still produce estimators of good quality (low bias and variance) relative to the minimum variance unbiased estimators for each distribution, at least when practical efficiency is considered.