Saddlepoint Approximation for Multivariate Cumulative Distribution Functions and Probability Computations in Sampling Theory and Outlier Testing
本文给出了多项分布、多元超几何分布、Dirichlet分布和多元Pólya分布这四种多元累积分布函数的二阶鞍点近似方法，并直接近似了矩形区域的概率，应用于异常值不一致性检验和滑动检验。
Abstract Four multivariate distributions commonly arise in sampling theory: the multinomial, multivariate hypergeometric, Dirichlet, and multivariate Pólya distributions. Second-order saddlepoint approximations are given for approximating these multivariate cumulative distribution functions (cdf's) in their most general settings. Probabilities of rectangular regions associated with these cdf's are also approximated directly using second-order saddlepoint methods. All the approximations follow from characterizations of the multivariate distributions as conditional distributions. Applications to outlier discordancy tests and slippage tests are discussed.