ON THE CUMULATIVE DISTRIBUTION FUNCTION OF THE VARIANCE-GAMMA DISTRIBUTION

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI:10.1017/s0004972723001387

ROBERT E. GAUNT

引用次数: 0

Abstract

We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From these formulas, we deduce exact formulas for the cumulative distribution function of the product of two correlated zero-mean normal random variables.

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关于方差-伽马分布的累积分布函数

我们得到了方差-伽马分布的累积分布函数的精确公式，即涉及修正的第二类贝塞尔函数和修正的第一类洛梅尔函数的无穷级数。根据这些公式，我们推导出两个相关零均值正态分布随机变量乘积的累积分布函数的精确公式。

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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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society