The variance-gamma distribution: A review

A Fischer, RE Gaunt, A Sarantsev - arXiv preprint arXiv:2303.05615, 2023 - arxiv.org
The variance-gamma (VG) distributions form a four-parameter family which includes as
special and limiting cases the normal, gamma and Laplace distributions. Some of the …

The basic distributional theory for the product of zero mean correlated normal random variables

RE Gaunt - Statistica Neerlandica, 2022 - Wiley Online Library
The product of two zero mean correlated normal random variables, and more generally the
sum of independent copies of such random variables, has received much attention in the …

Observations on the McKay Iν Bessel distribution

K Górska, A Horzela, DJ Maširević… - Journal of mathematical …, 2022 - Elsevier
The main aim of this article is to derive new representation formulae for CDF of random
variable distributed according to the McKay I ν Bessel law: first set of formulae are given in …

On the cumulative distribution function of the variance-gamma distribution

RE Gaunt - Bulletin of the Australian Mathematical Society, 2024 - cambridge.org
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 product distribution of more-than-two correlated normal variables: A didactic review with some new findings

H Ogasawara - Communications in Statistics-Theory and Methods, 2024 - Taylor & Francis
Some reviews of the distribution of the product of two correlated normal random variables
and the corresponding more-than-two uncorrelated cases are given with a historical …

Extended Exton's triple and Horn's double hypergeometric functions and associated bounding inequalities

RK Parmar, J Choi - Symmetry, 2023 - mdpi.com
This paper introduces extensions H 4, p and X 8, p of Horn's double hypergeometric function
H 4 and Exton's triple hypergeometric function X 8, taking into account recent extensions of …

The McKay Bessel distribution revisited

D Jankov Maširević - Fractional Calculus and Applied Analysis, 2024 - Springer
Bearing in mind an increasing popularity of the fractional calculus the main aim of this paper
is to derive several new representation formulae for the cumulative distribution function (cdf) …

Bounds for confluent Horn function Φ2 deduced by McKay Iν Bessel law

D Jankov Maširević, TK Pogány - Rad Hrvatske akademije znanosti i …, 2023 - hrcak.srce.hr
Sažetak The main aim of this article is to derive by probabilistic method new functional and
uniform bounds for Horn confluent hypergeometric Φ2 of two variables and the incomplete …

Bounds for incomplete confluent Fox–Wright generalized hypergeometric functions

TK Pogány - Mathematics, 2022 - mdpi.com
We establish several new functional bounds and uniform bounds (with respect to the
variable) for the lower incomplete generalized Fox–Wright functions by means of the …

Probabilistic and Analytical Aspects of the Symmetric and Generalized Kaiser–Bessel Window Function

Á Baricz, TK Pogány - Constructive approximation, 2023 - Springer
Abstract The generalized Kaiser–Bessel window function is defined via the modified Bessel
function of the first kind and arises frequently in tomographic image reconstruction. In this …