Closed‐form maximum likelihood estimator for logarithmic distribution and its asymptotic variance

Abstract This paper presents the exact analytical solution to the long‐standing problem of determining the maximum likelihood estimator (MLE) for the parameter of the logarithmic distribution. Despite having been introduced more than 80 years ago, no one has derived an explicit MLE for the logarithmic distribution parameter. In addition to this primary result, we also derive the MLE asymptotic variance and provide other related findings that further contribute to the understanding of this distribution.