A new discrete probability distribution with integer support on (−∞, ∞)

ABSTRACT

A new discrete probability distribution with integer support on (−∞, ∞) is proposed as a discrete analog of the continuous logistic distribution. Some of its important distributional and reliability properties are established. Its relationship with some known distributions is discussed. Parameter estimation by maximum-likelihood method is presented. Simulation is done to investigate properties of maximum-likelihood estimators. Real life application of the proposed distribution as empirical model is considered by conducting a comparative data fitting with Skellam distribution, Kemp's discrete normal, Roy's discrete normal, and discrete Laplace distribution.

KEYWORDS:

• Characterization
• discrete laplace distribution
• discrete logistic distribution
• discrete normal distribution
• failure rate
• model selection
• survival function

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62F10

Acknowledgments

The authors would like to acknowledge the Associate Editor and both the anonymous referees for the comments and suggestions which resulted in substantial improvement in the material and presentation of the paper.