A New Generalization of the Logarithmic Distribution Arising from the Inverse Trinomial Distribution

Abstract

A new generalization of the logarithmic distribution (LD)—the generalized logarithmic distribution (GLD)—is introduced. The GLD is a cluster size distribution of the inverse trinomial distribution, which arises in a generalized random walk problem. Major properties of the GLD are derived and discussed. The method of first moment and frequency of one count and maximum likelihood estimation (MLE) are used for parameter estimation. Rao's score test statistic is derived as a model selection tool. Finally, we demonstrate an application of the GLD in fitting insect data from temperate and tropical regions.