有关相关正态随机变量积分布的渐近展开式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-06-11 DOI:10.1111/sapm.70070

Robert E. Gaunt, Zixin Ye

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引用次数: 0

摘要

本文导出了两个非零均值和任意方差的相关正态随机变量乘积的尾部分布的渐近展开式，以及这些随机变量的独立副本之和的渐近展开式。给出了分位数函数的渐近逼近。数值结果验证了渐近逼近的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotic Expansions Relating to the Distribution of the Product of Correlated Normal Random Variables

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with nonzero means and arbitrary variances, and more generally the sum of independent copies of such random variables. Asymptotic approximations are also given for the quantile function. Numerical results are given to test the performance of the asymptotic approximations.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.