A modified closed-form maximum likelihood estimator

The maximum likelihood estimator plays a fundamental role in statistics. However, for many models, the estimators do not have closed-form expressions. This limitation can be significant in situations where estimates and predictions need to be computed in real-time, such as in applications based on embedded technology, in which numerical methods can not be implemented. This paper provides a modification in the maximum likelihood estimator that allows us to obtain the estimators in closed-form expressions under some conditions. Under mild conditions, the estimator is invariant under one-to-one transformations, consistent, and has an asymptotic normal distribution. The proposed modified version of the maximum likelihood estimator is illustrated on the Gamma, Nakagami, and Beta distributions and compared with the standard maximum likelihood estimator.