A New Method of Estimation of Size-Biased Generalized Logarithmic Series Distribution

Khurshid Ahmad Mir*
Department of Statistics, Govt. Degree College (Boys) Baramulla, Kashmir, India.

© 2009 Mir et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Statistics, Govt. Degree College (Boys) Baramulla, Kashmir, India. E-mail:


In this paper, a size-biased generalized logarithmic series distribution (SBGLSD) is introduced and its moments are obtained. The estimates of the parameters of SBGLSD are obtained by employing the method of moments and a proposed new method of estimation. The new proposed method of estimation uses the non-zero frequency of a variable only up to a finite value. In this method, the estimation of only one parameter is needed and of the other is obtained by the relationship among the parameters by counting the number of non-zero frequency classes. The method is found very simple and quick to apply in practice. Extensive simulations are performed to compare the performances of the proposed and the moment method of estimation mainly with respect to their biases and mean squared errors (MSE’s), for different sample sizes and of different parametric values. Comparison has been made among different estimation methods by means of Pearson’s Chi-square, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) techniques.

Keywords: Size-biased generalized logarithmic series distribution, Non- zero frequency classes, Chi-square AIC, BIC..