AN ALTERNATIVE TO 'THE LOGARITHMIC-WITH-ZEROS DISTRIBUTION' AND ITS GENERALIZATION: PROPERTIES AND ESTIMATION

摘要

Through this article we propose a class of distributions namely "the alpha-logarithmic series distribution (ALSD)" as an alternative to "the logarithmic-with-zeros distribution" of Kha-tri (1961) and develop a generalization of it and call it "the generalized alpha-logarithmic series distribution (GALSD)". Several properties of these classes of distributions are studied here. The maximum likelihood estimation of the parameters of the GALSD is discussed and fitted to certain real life data sets for illustrating its usefulness compared to the existing models. Further, the generalized likelihood ratio test is considered for testing the significance of the additional parameter of the GALSD model and a simulation study is carried out for assessing the performance of the estimators of each parameter of the model.