The bivariate logarithmic series distribution

Abstract

The bivariate logarithmic series distribution was introduced by Subrahmaniam (1966) as a Fisher-limit to the bivariate negative binomial distribution. The present paper considers the properties of the distribution along with various models giving rise to it. Problems of estimation and the goodness-of-fit are examined. Methods for simulating the distribution are developed and illusuated.

Keywords:

• bivariate negative binomial distribution
• bivariate logarithmic series distribution
• compounding
• Fisher-limit
• goodness-of-fit tests
• modified logarithmic series distribution
• probability generating function
• Neyman' C(α) test
• Rao's efficient score test
• simulation