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ON THE CUMULATIVE DISTRIBUTION FUNCTION OF THE VARIANCE-GAMMA DISTRIBUTION

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  29 January 2024

ROBERT E. GAUNT Open the ORCID record for ROBERT E. GAUNT [Opens in a new window]
ROBERT E. GAUNT*
Affiliation:
Department of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
e-mail: robert.gaunt@manchester.ac.uk
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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.

Keywords

variance-gamma distributioncumulative distribution functionproduct of correlated normal random variablesmodified Bessel functionmodified Lommel function

MSC classification

Primary: 62E15: Exact distribution theory
Secondary: 60E05: Distributions

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 2 , October 2024 , pp. 389 - 397
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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