On Methods of Estimation for Generalized Logarithmic Series Distribution and Its Application to Counts of Red Mites on Apple Leaves

The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

On size-biased Consul distribution

In this paper, a size-biased Consul distribution (SBCOND) is defined. Recurrence relations for central moments and the moments about origin are obtained. Different estimation methods for the parameters of the model are discussed. A comparative analysis is done among the three different estimation methods and the proposed model is compared with the generalized logarithmic series distribution (GLSD) and simple Consul distribution.

On size-biased generalized logarithmic series distribution

In this paper a size-biased generalized logarithmic series distribution (SBGLSD), a particular case of the weighted generalized logarithmic series distribution, taking the weights as the variate values is defined. The moments and recurrence relation of SBGLSD are obtained. We have also established the relationship between the moments of size-biased generalized logarithmic series distribution and size-biased generalized geometric series distribution (SBGGSD). Bayesian estimation of SBGLSD is discussed and a comparison is made with the generalized logarithmic series distribution (GLSD) by using the Monte Carlo simulation technique.