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The method of moments for multivariate random sums in the Poisson-Skew-Normal case

Javed, Farrukh LU ; Loperfido, Nicola and Mazur, Stepan LU (2025) In Statistics and Probability Letters 219.
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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fourth cumulant, Kurtosis, Poisson distribution, Skew-normal distribution
in
Statistics and Probability Letters
volume
219
article number
110338
publisher
Elsevier
external identifiers
  • scopus:85212330926
ISSN
0167-7152
DOI
10.1016/j.spl.2024.110338
language
English
LU publication?
yes
id
0020abf4-97a0-4b6e-bad0-82e237d2b7e7
date added to LUP
2025-03-04 10:43:42
date last changed
2025-04-04 14:42:35
@article{0020abf4-97a0-4b6e-bad0-82e237d2b7e7,
  abstract     = {{<p>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.</p>}},
  author       = {{Javed, Farrukh and Loperfido, Nicola and Mazur, Stepan}},
  issn         = {{0167-7152}},
  keywords     = {{Fourth cumulant; Kurtosis; Poisson distribution; Skew-normal distribution}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Statistics and Probability Letters}},
  title        = {{The method of moments for multivariate random sums in the Poisson-Skew-Normal case}},
  url          = {{http://dx.doi.org/10.1016/j.spl.2024.110338}},
  doi          = {{10.1016/j.spl.2024.110338}},
  volume       = {{219}},
  year         = {{2025}},
}