The Discrete Normal Distribution

Abstract

The normal distribution has been playing a key role in stochastic modeling for a continuous setup. But its distribution function does not have an analytical form. Moreover, the distribution of a complex multicomponent system made of normal variates occasionally poses derivational difficulties. It may be worth exploring the possibility of developing a discrete version of the normal distribution so that the same can be used for modeling discrete data. Keeping in mind the above requirement we propose a discrete version of the continuous normal distribution. The Increasing Failure Rate property in the discrete setup has been ensured. Characterization results have also been made to establish a direct link between the discrete normal distribution and its continuous counterpart. The corresponding concept of a discrete approximator for the normal deviate has been suggested. An application of the discrete normal distributions for evaluating the reliability of complex systems has been elaborated as an alternative to simulation methods.

Keywords:

• Life distribution
• Discrete models
• Normal distribution
• Class properties
• Normal approximator
• Probability evaluation
• Stress-strength analysis

Acknowledgments

The author is thankful to the referees for their valuable comments and to CSIR for financial support under research grant no 25(0104)/99/EMR-II.