On Size-Biased Logarithmic Series Distribution and Its Applications

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

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© 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. College (Boys), Baramulla, Kashmir, India. Tel: 91-1942426584; Fax: 91-19424265; E-mail:


In this paper, a size-biased logarithmic series distribution (SBLSD), a particular case of the weighted logarithmic series distribution, taking the weights as the variate values is defined. The moments and recurrence relation of (SBLSD) are obtained. Negative moments and inverse ascending factorial moments of the size-biased logarithmic series distribution have been derived in terms of hyper-geometric function. Recurrence relations for these moments have also been derived using properties of hyper-geometric functions. Different estimation methods for the parameter of the model are discussed. R- Software has been used for making a comparison among the three different estimation methods and with the logarithmic series distribution.

Keywords: Size-biased logarithmic series distribution, Negative moments, Inverse ascending factorial moments, Bayes’ estimator, Beta distribution, R-Software..