Details
| Original language | English |
|---|---|
| Article number | 105154 |
| Journal | Journal of multivariate analysis |
| Volume | 195 |
| Early online date | 30 Dec 2022 |
| Publication status | Published - 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
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Numerical Analysis
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of multivariate analysis, Vol. 195, 105154, 05.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A goodness-of-fit test for the compound Poisson exponential model
AU - Baringhaus, Ludwig
AU - Gaigall, Daniel
N1 - Funding information: The authors thank the Editor, the Associate Editor and the referees for constructive comments and suggestions.
PY - 2023/5
Y1 - 2023/5
N2 - 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.
AB - 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.
KW - Bootstrapping
KW - Collective risk model
KW - Compound Poisson exponential model
KW - Goodness-of-fit
UR - http://www.scopus.com/inward/record.url?scp=85145833324&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2022.105154
DO - 10.1016/j.jmva.2022.105154
M3 - Article
AN - SCOPUS:85145833324
VL - 195
JO - Journal of multivariate analysis
JF - Journal of multivariate analysis
SN - 0047-259X
M1 - 105154
ER -