The Method of Moments for Multivariate Random Sums

Farrukh Javed (), Nicola Loperfido and Stepan Mazur
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Farrukh Javed: Lund University, Postal: Lund University, Department of Statistics, Tycho Brahes väg 1, 223 63 Lund, Sweden, https://www.lunduniversity.lu.se/lucat/user/b8c8d0f7315437248f5d744dfc64eb72

No 2024:6, Working Papers from Örebro University, School of Business

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. (search for similar items in EconPapers)
JEL-codes: C13 C30 C46 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2024-06-18
New Economics Papers: this item is included in nep-ecm
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