Vol. 46 No. 2 (2025), Статьи
Vol. 46 No. 2 (2025)

CHARACTERISTIC FUNCTION OF THE SUM OF COPULA-DEPENDENT POISSON RANDOM VARIABLES: GENERAL THEORY AND APPLICATIONS TO ARCHIMEDEAN AND GAUSSIAN COPULAS

Статьи
Published 2025-12-18
  • Dushatov N.T.
Dushatov N.T.
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Keywords

Keywords: Poisson distribution; copula dependence; discrete copula; characteristic function; dependent counts; Archimedean copula; Gaussian copula; multivariate discrete distributions

How to Cite

Dushatov N.T. “CHARACTERISTIC FUNCTION OF THE SUM OF COPULA-DEPENDENT POISSON RANDOM VARIABLES: GENERAL THEORY AND APPLICATIONS TO ARCHIMEDEAN AND GAUSSIAN COPULAS”. World Scientific Research Journal 46, no. 2 (December 18, 2025): 233–244. Accessed July 16, 2026. https://openresearch-hub.com/index.php/wsrj/article/view/869.
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Abstract

Abstract. This paper derives a closed-form representation for the characteristic function of the sum , where  and  are Poisson random variables connected through an arbitrary bivariate copula. While the sum of independent Poisson variables remains Poisson-distributed, dependence—introduced via a discrete copula—fundamentally alters the distributional structure of . Using the discrete version of Sklar’s theorem and a difference-operator representation of copulas for count data, we establish an exact series formula for the characteristic function of  under completely general dependence. Furthermore, we develop explicit analytic expressions for three Archimedean copulas (Clayton, Frank, and Gumbel) and provide a numerically tractable representation for the Gaussian copula using the distributional transform approach. Numerical experiments confirm that different forms of dependence create distinct signatures in the characteristic function, highlighting its usefulness for modeling dependent count data in insurance, hydrology, and reliability applications.

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