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Abstract
In this thesis, we propose a method to approximate discrete distributions based on Provost, Jiang, and Ha’s paper. The probability mass function approximants are expressed as product of an appropriate base density function and a rational adjustment. This approach, which is based on a moment-matching technique, is not only conceptually straight forward but easy to perform. The methodology is applied to certain discrete random distributions, the approximations are in excellent agreement with the exact values. Another method based on moment-generating-function-matching technique is raised as well. This approach requires less computation work than previous method but gives comparable approximations. It is applied to the binomial distribution. Widely applications are left to future research.
