Document Type
Article
Publication Date
9-2019
Publisher
Statistical Research and Training Center
Source Publication
Journal of Statistical Research of Iran
Source ISSN
1735-1294
Abstract
In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes.
Recommended Citation
Rasekhi, Mahdi and Hamedani, Gholamhossein, "Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations" (2019). Mathematical and Statistical Science Faculty Research and Publications. 70.
https://epublications.marquette.edu/math_fac/70
Comments
Published version. Journal of Statistical Research of Iran, Vol. 16, No. 1 (September 2019): 59-72. DOI. © 2019 Statistical Research and Training Center. Used with permission.