The Alpha-Logarithmic Series Distribution of Order

Abstract

Here we develop an order k version of the alpha-logarithmic series distribution of Kumar and Riyaz (South African Statist. J., 2014) through its probability generating function and derive its probability mass function, mean and variance. The parameters of the model are estimated by the method of maximum likelihood and the distribution has been fitted to certain real life data sets. Certain test procedures are considered for testing the significance of the additional parameters of the distribution. In addition, a simulation study is conducted for assessing the performance of the likelihood estimators of each of the parameters of the model.

Keywords

• Count data models; generalized likelihood ratio test; logarithmic series distribution; maximum likelihood estimation; Markov chain Monte Carlo simulation; probability generating function; Rao’s efficient score test.