A goodness-of-fit test for the compound Poisson exponential model

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Authors

  • Ludwig Baringhaus
  • Daniel Gaigall

External Research Organisations

  • FH Aachen University of Applied Sciences
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Details

Original languageEnglish
Article number105154
JournalJournal of multivariate analysis
Volume195
Early online date30 Dec 2022
Publication statusPublished - May 2023

Abstract

On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.

Keywords

    Bootstrapping, Collective risk model, Compound Poisson exponential model, Goodness-of-fit

ASJC Scopus subject areas

Cite this

A goodness-of-fit test for the compound Poisson exponential model. / Baringhaus, Ludwig; Gaigall, Daniel.
In: Journal of multivariate analysis, Vol. 195, 105154, 05.2023.

Research output: Contribution to journalArticleResearchpeer review

Baringhaus L, Gaigall D. A goodness-of-fit test for the compound Poisson exponential model. Journal of multivariate analysis. 2023 May;195:105154. Epub 2022 Dec 30. doi: 10.1016/j.jmva.2022.105154
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