Bernoulli Distribution: Important Properties and Comparison of Estimation Methods
Keywords:
Bernoulli Distribution, Maximum Likelihood Estimation, Bayes method, Point Estimation, Regression ModelsAbstract
The Bernoulli distribution (BD) is a fundamental member of the binary distribution family, with widespread and impactful applications across various fields. It plays a pivotal role in the construction of zero-inflated (ZI) distributions, which require a two-process framework - one of which is governed by the BD. This study aims to explore the key properties of the BD and evaluate the performance of three widely used parameter estimation techniques: Method of Moments (MM), Maximum Likelihood Estimation (MLE), and Bayesian Method (BM). Through extensive simulation studies and analysis of real-world datasets, we assess the accuracy and practicality of each method. The results demonstrate that both MLE and BM yield highly reliable estimates, with MLE offering a more straightforward implementation. Consequently, MLE may be preferable in scientific applications where ease of use is a priority.References
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