Saddlepoint Approximations to the CDF of Some Statistics with Nonnormal Limit Distributions
本文研究将鞍点逼近中的正态基分布替换为任意基分布，详细考察卡方基和逆高斯基，并通过两个例子（卡方变量线性组合、随机游走首次通过时间分布）比较逼近精度。
Abstract In standard saddlepoint approximations to the cumulative distribution function of a random variable, the normal distribution has appeared to play a special role. In this article we consider what happens when the normal “base” distribution is replaced by an arbitrary base distribution. Generalized versions of several standard formulas, are presented. The choice of a chi-squared base or an inverse Gaussian base is then considered in detail. The generalized approximations are compared in two examples: a linear combination of chi-squared variables and the first passage time distribution for a random walk. The former example considers approximations using the chi-squared base that are slightly more accurate than their normal-based counterparts. In the latter example, approximations based on the inverse Gaussian are considerably more accurate than their normal-based counterparts.