Exact analysis of discrete data is a computationally intensive exercise. The key role of modern computing power in making it accessible to the data analyst is not in doubt. Nonetheless, without eﬃcient algorithms and sound implementation, it would still remain infeasible, especially for multivariate data problems. This chapter starts the presentation of computational issues and algorithms relating to exact conditional analysis of discrete data. The goal is to present methods for computing the probability distributions and tools of inference described in the previous chapters, and to lay a foundation upon which eﬃcient algorithms for exact analysis of more complex data will later be constructed. Its speciﬁc aims are to present:
• Algorithms for computing the factorial, binomial, Poisson, hypergeometric and negative binomial coeﬃcients, distributions and their tail areas.