Some Methods of Estimation for the Logarithmic Series Distribution

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Abstract
Applications of the logarithmic series distribution have been discussed among others by Fisher, Williams, Harrison and Kendall. Problems of estimation, however, do not seem to have been much investigated. In this paper, different estimates for the parameter of the distribution are suggested. Their efficiencies and amounts of bias, if any, are investigated. Numerical results are given for selected special cases. The estimates considered are as follows: Maximum Likelihood Estimate, Ratio Estimate, Two-Moments Estimate and First Moment First Cell Estimate.