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首页> 外文期刊>Canadian Journal of Pure and Applied Sciences >SADDLEPOINT APPROXIMATION TO CUMULATIVE DISTRIBUTION FUNCTIONS FOR SOME DIFFICULT AND UNKNOWN LINEAR COMBINATIONS OF RANDOM VARIABLES
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SADDLEPOINT APPROXIMATION TO CUMULATIVE DISTRIBUTION FUNCTIONS FOR SOME DIFFICULT AND UNKNOWN LINEAR COMBINATIONS OF RANDOM VARIABLES

机译：一些随机变量的困难和未知线性组合的累积分布函数的鞍点逼近

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摘要

Approximations are very important because it is sometimes not possible to obtain an exact representation of the probability distribution function (PDF) and the cumulative distribution function (CDF). Even when true (exact) representations are possible, approximations, in some cases, simplify the analytical treatments. In this paper, we extend the known saddlepoint tail probability approximations to univariate cases, including univariate conditional cases. Our first approximation (the weighted random sum applies to unknown and very difficult statistics (we discuss the approximations within the random sum Poisson-Exponential random variables).We evaluate the performance of the saddlepoint approximation using simulations. Our second approximation (convolutions of Gamma random variables, ), are difficult to obtain. These computations are also compared with the exact and normal approximations. We find that the saddlepoint methods provide very accurate approximations for the CDFs probabilities that surpass other methods of approximation, such as normal approximation.The third approximation, including conditional saddlepoint approximations, uses the double saddlepoint. To demonstrate the methods of conditioning in statistical inference, we find a mid p-value using a conditionalsaddlepoint approximation for percentile modified linear rank tests. We show that in the double saddlepoint case, the saddlepoint approximations demonstrate better accuracy than the normal approximation while sharing the same accuracy.
机译：近似值非常重要，因为有时无法获得概率分布函数（PDF）和累积分布函数（CDF）的精确表示。即使可以使用正确的（精确的）表示，在某些情况下，近似值也可以简化分析处理。在本文中，我们将已知的鞍点尾部概率近似扩展到单变量情况，包括单变量条件情况。我们的第一个近似值（加权随机和适用于未知且非常困难的统计数据（我们讨论了随机和泊松指数随机变量中的近似值）。我们使用模拟评估鞍点近似的性能。第二个近似值（伽玛随机卷积我们很难发现这些鞍点方法为CDFs概率提供了非常精确的近似值，这些CDF概率超过了其他近似方法，例如正态近似值。包括条件鞍点近似，使用了双鞍点，为了说明统计推断的条件方法，我们使用百分位数修改线性秩检验使用了条件鞍点近似来找到一个中间p值，这表明在双鞍点情况下，鞍点近似值证明更好acy比普通近似法共享相同的精度。

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