方差-乘积分布。

IF 1.2 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2025-01-01 Epub Date: 2025-09-23 DOI:10.1007/s00025-025-02499-y

Robert E Gaunt, Siqi Li, Heather L Sutcliffe

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引用次数: 0

摘要

我们导出了N个独立方差-伽马随机变量与零位置参数乘积的精确概率密度函数。然后，我们应用该公式推导出累积分布函数和特征函数的公式，以及密度、尾概率和分位数函数的渐近逼近。根据我们的一般结果，我们推导了N个独立非对称拉普拉斯随机变量的乘积和独立拉普拉斯与中心正态随机变量的混合乘积的密度、累积分布函数和特征函数的封闭形式公式。

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The Variance-Gamma Product Distribution.

We derive the exact probability density function of the product of N independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and characteristic function, as well as asymptotic approximations for the density, tail probabilities and quantile function. From our general results, we deduce closed-form formulas for the density, cumulative distribution function and characteristic function of the product of N independent asymmetric Laplace random variables and mixed products of independent Laplace and centred normal random variables.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.