Generalizations of Log-Series Distribution with Applications

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Ram C. Tripathi*+
• Companies: The University of Texas at San Antonio
• Keywords: Log-series ; Generalized log-series ; Length-baised sampling ; Generalized geometric ; Statistics inference

Abstract

The log-series distribution is used as a model to describe the species abundance data such as the distribution of moths and tropical butterflies. These types of data typically have long tails. In practice, however, there are data with even longer tails which cannot be described well by the ordinary log-series. There are several generalizations of log-series in the literature based on extensions of negative binomial type models. Another phenomenon commonly encountered in long-tailed data is the effect of length-biased sampling: 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 modeling long-tailed data. In this paper, we present two generalizations of log-series distribution and study their characteristics. We also derive corresponding generalized geometric distributions arising from these models. We develop methods of statistical inference regarding their parameters, and present examples to provide applications to real data.