Approximations of the binomial distribution.

Thesis (M.A.)--Boston UniversityThis thesis provides a discussion of various approximations to the cumulative binomial distribution. We begin our analysis with the discussion of the simple normal approximation, based on the DeMoivre-Laplace Limit Theorem. This theorem states that the binomial distribution converges to the normal distribution in the situation wherein we hold p constant and allow n --> inf. The simple normal approximation is the most widely used of all approximations , because of its simplicity and the availability of the necessary tables. However, its importance goes far beyond the domain of numerical calculation. We also show how the simple normal approximation may be used to obtain confidence intervals for the parameter p. We note various transformations that can be used to transform the binomial distribution into the normal distribution. In particular we mention the arcsine approximation which is based on the variance stabilizing angular transformation. [TRUNCATED