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JSRI 2019, 16(1): 59-72 Back to browse issues page
Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations
Mahdi Rasekhi *1, Gholamhossein G. Hamedani
1- , rasekhimahdi@gmail.com
Abstract:   (87 Views)

 
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.
 
 
 
 
Keywords: Cox-Snell bias-correction, Bootstrap bias-correction, Logarithmic series distribution, Maximum likelihood estimator, Monte Carlo simulation.
Full-Text [PDF 487 kb]   (11 Downloads)    
Type of Study: Research | Subject: General
Received: 2019/09/8 | Accepted: 2020/10/7 | Published: 2019/09/19
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Rasekhi M, G. Hamedani G. Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations. JSRI. 2019; 16 (1) :59-72
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Volume 16, Issue 1 (9-2019) Back to browse issues page
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