Discrete Beta-Exponential Distribution

Abstract

There are not many known distributions for modeling discrete data. In this paper, we shall introduce a discrete analogue of the beta-exponential distribution of Nadarajah and Kotz (2006), which is more plausible in modeling discrete data and exhibits both increasing and decreasing hazard rates. The discrete beta-exponential distribution can be viewed as a generalization of the discrete generalized exponential distribution introduced by Nekoukhou et al. (2012) and, thus, as an another generalization of the geometric distribution. We shall first study some basic distributional and moment properties of the new distribution. Then, certain structural properties of the distribution such as its unimodality, hazard rate behavior, and Rényi entropy are discussed. Using the maximum likelihood method, estimation of the model parameters is also investigated. Finally, the model is examined with a real data set and compared with its rival model, that is, the discrete generalized exponential distribution.

Keywords:

• Discrete generalized exponential distribution
• Entropy
• Generalized exponential distribution
• Geometric distribution
• Hazard rate
• Unimodality.

Mathematics Subject Classification:

• 60E05; 62E10