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Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach

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Abstract

We develop a likelihood-ratio test for discriminating between the g-and-h and the g distribution, which is a special case of the former obtained when the parameter h is equal to zero. The g distribution is a shifted lognormal, and is therefore suitable for modeling economic and financial quantities. The g-and-h is a more flexible distribution, capable of fitting highly skewed and/or leptokurtic data, but is computationally much more demanding. Accordingly, in practical applications the test is a valuable tool for resolving the tractability-flexibility trade-off between the two distributions. Since the classical result for the asymptotic distribution of the test is not valid in this setup, we derive the null distribution via simulation. Further Monte Carlo experiments allow us to estimate the power function and to perform a comparison with a similar test proposed by Xu and Genton (Comput Stat Data Anal 91:78–91, 2015). Finally, the practical relevance of the test is illustrated by two risk management applications dealing with operational and actuarial losses.

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Acknowledgements

We thank dr. Fabio Piacenza (UniCredit SpA) for providing us with the operational risk data and dr. Ganggang Xu for sharing the codes used in Xu and Genton (2015). Julien Hambuckers acknowledges the financial support of the National Bank of Belgium. We also thank two anonymous reviewers for valuable comments on an earlier version of this paper.

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Authors and Affiliations

  1. Department of Economics and Management, University of Trento, Trento, Italy

    Marco Bee

  2. Department of Finance, HEC Liège, University of Liège, Liège, Belgium

    Julien Hambuckers

  3. Department of Economics, University of Verona, Verona, Italy

    Flavio Santi

  4. Department of Statistical Sciences “P. Fortunati”, University of Bologna, Bologna, Italy

    Luca Trapin

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  1. Marco Bee
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  2. Julien Hambuckers
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  3. Flavio Santi
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  4. Luca Trapin
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Correspondence to Marco Bee.

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The R codes used for the computations in this paper are available at http://marcobee.weebly.com.

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Bee, M., Hambuckers, J., Santi, F. et al. Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach. Comput Stat 36, 2177–2200 (2021). https://doi.org/10.1007/s00180-021-01078-3

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