An Improvement in Maximum Likelihood Estimation of the Gompertz Distribution Parameters

In this study, we will look at estimating the parameters of the Gompertz distribution. We know that the maximum likelihood technique is the most often used method in the literature for parameter estimation. However, it is well known that the maximum likelihood estimators (MLEs) are biased for small sample sizes. As a result, we are motivated to produce nearly unbiased estimators for the parameters of this distribution. To be more specific, we concentrate on two bias-correction strategies (analytical and bootstrap approaches) to minimize MLE biases to the second order of magnitude. Monte Carlo simulations are used to compare the performances of these estimators. Finally, two real-data examples are offered to demonstrate the utility of our proposed estimators in small sample sizes.