On the cumulative distribution function of the variance-gamma distribution
Robert E. Gaunt
TL;DR
This paper derives exact formulas for the cumulative distribution function of the variance-gamma distribution using special functions, and applies these results to the distribution of the product of two correlated normal variables.
Contribution
It provides novel exact formulas for the variance-gamma CDF involving Bessel and Lommel functions, and extends these to correlated normal products.
Findings
Exact formulas for the variance-gamma CDF as infinite series.
Formulas for the distribution of the product of two correlated normal variables.
Enhanced understanding of the distributional properties of variance-gamma and related variables.
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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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Bayesian Methods and Mixture Models · Mathematical functions and polynomials