An improvement in maximum likelihood estimation of the Burr XII distribution parameters

In this paper, we discuss the parameters estimation of the Burr XII distribution. We know that the most popular method in the literature for parameter estimation is the maximum likelihood method. However, the maximum likelihood estimators (MLEs) are widely known to be biased for small sample sizes. Therefore, this motivate us to obtain approximately unbiased estimators for this distribution' parameters. Precisely, we focus on two bias-correction techniques (analytical and bootstrap approaches) to reduce the biases of the MLEs to the second order of magnitude. In order to compare the performance of these estimators, Monte Carlo simulations are conducted. Lastly, two real-data examples are provided to show the usefulness of these proposed estimators when sample sizes are small.