Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/300308 
Year of Publication: 
2024
Series/Report no.: 
Working Paper No. 6/2024
Publisher: 
Örebro University School of Business, Örebro
Abstract: 
Multivariate random sums appear in many scientific fields, most notably 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 expressions for some fundamental measures of multivariate kurtosis and highlight some limitations of both projection pursuit and invariant coordinate selection.
Subjects: 
Fourth cumulant
Kurtosis
Poisson distribution
Skew-normal distribution
JEL: 
C13
C30
C46
Document Type: 
Research Report

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