A New Discrete Exponential Family of Distributions: Properties and Application to Power Series Distributions

SYNOPTIC ABSTRACT

This paper introduces a discrete exponential family distribution which includes the important classes of series distributions - generalized power series distributions, modified power series distributions, and power series distributions associated with the Lagrange expansion. This provides a unified approach for the study of these three classes of power series distributions. After discussing moments, recurrsion relations, and maximum likelihood estimation for the discrete exponential family, the results are applied to certain well-known discrete distributions like the generalized Poisson, negative binomial and logarithmic series distributions, and the lost games distribution. A new discrete distribution termed linear function binomial distribution is introduced and its properties studied.

Key Words and Phrases:

• Discrete exponential family
• Power series distributions - GPSD MPSD, LPSD
• moment properties
• ML estimation