Scandinavian Working Papers in Economics

Working Papers,
Örebro University, School of Business

No 2024:6: The Method of Moments for Multivariate Random Sums

Farrukh Javed (), Nicola Loperfido () and Stepan Mazur ()
Additional contact information
Farrukh Javed: Lund University, Postal: Lund University, Department of Statistics, Tycho Brahes väg 1, 223 63 Lund, Sweden
Nicola Loperfido: Università degli Studi di Urbino "Carlo Bo", Postal: Dipartimento di Economia, Società e Politica, Università degli Studi di Urbino "Carlo Bo", 61033 ITALY
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden

Abstract: Multivariate random sums appear in many scienti c elds, most no- tably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case, thus preventing likelihood inference. In this paper, we address the problem by the method of moments, under the assumption that the claim size and the claim number have a multivariate skew-normal and a Poisson distribution, respectively. In doing so, we also derive closed-form expres- sions for some fundamental measures of multivariate kurtosis and high- light some limitations of both projection pursuit and invariant coordinate selection.

Keywords: Fourth cumulant; Kurtosis; Poisson distribution; Skew-normal distribution.

JEL-codes: C13; C30; C46

Language: English

13 pages, June 18, 2024

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