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Risks 2018, 6(3), 70;

Log-Normal or Over-Dispersed Poisson?

Department of Economics, University of Oxford & Oriel College, Oxford OX1 4EW, UK
Received: 18 June 2018 / Revised: 5 July 2018 / Accepted: 6 July 2018 / Published: 9 July 2018
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Although both over-dispersed Poisson and log-normal chain-ladder models are popular in claim reserving, it is not obvious when to choose which model. Yet, the two models are obviously different. While the over-dispersed Poisson model imposes the variance to mean ratio to be common across the array, the log-normal model assumes the same for the standard deviation to mean ratio. Leveraging this insight, we propose a test that has the power to distinguish between the two models. The theory is asymptotic, but it does not build on a large size of the array and, instead, makes use of information accumulating within the cells. The test has a non-standard asymptotic distribution; however, saddle point approximations are available. We show in a simulation study that these approximations are accurate and that the test performs well in finite samples and has high power. View Full-Text
Keywords: non-nested testing; encompassing; chain-ladder non-nested testing; encompassing; chain-ladder

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Harnau, J. Log-Normal or Over-Dispersed Poisson? Risks 2018, 6, 70.

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