A Generalization of the Log-series Distribution with Applications

• Activity Number: 317
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section*
• Author(s): Ram Tripathi*+ and Ramesh Gupta
• Affiliation(s): University of Texas, San Antonio and University of Maine
• Keywords: generalized log-series ; generalized negative binomial ; generalized geometric ; long-tailed data

Abstract

The log-series model was developed to describe long-tailed data, such as the distribution of catches of moths and of tropical butterflies. It is obtained as the limit of a zero-truncated negative binomial. However, there are data with longer tails, which can not be described well by the log-series model. There have been generalizations of the log-series distribution in the literature based on some of the extensions of the negative binomial. Another phenomenon resulting in long-tailed data is the length-biased sampling in the sense that the larger the number of species included in the study, the larger will be the chance to observe more of them, thus making it extra long-tailed. Length-biasing log-series and generalized log-series results in geometric and generalized geometric distributions, which are also suitable for modelling long-tailed data. In this paper, we develop an extension of the log-series distribution and its length-biased version, based on a new generalized negative binomial of Gupta and Ong. We develop statistical inference for these models and compare their fits with those obtained by some competing models utilizing long-tailed data.