Corrected Maximum Likelihood Estimations of the Lognormal Distribution Parameters

Abstract

As a result of asymmetry in practical problems, the Lognormal distribution is more suitable for data modeling in biological and economic fields than the normal distribution, while biases of maximum likelihood estimators are regular of the order O ( n − 1 ) , especially in small samples. It is of necessity to derive logical expressions for the biases of the first-order and nearly consistent estimators by bias correction techniques. Two methods are adopted in this article. One is the Cox-Snell method. The other is the resampling method known as parametric Bootstrap. They can improve maximum likelihood estimators performance and correct biases of the Lognormal distribution parameters. Through Monte Carlo simulations, we obtain average root mean squared error and bias, which are two important indexes to compare the effect of different methods. The numerical results reveal that for small and medium-sized samples, the performance of analytical bias correction estimation is superior than bootstrap estimation and classical maximum likelihood estimation. Finally, an example is given based on the actual data.