Modelling losses and locating the tail with the Pareto Positive Stable distribution |
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| Affiliation: | 1. Department of Neurosurgery, Medical College of Wisconsin, 8701 Watertown Plk Rd., Milwaukee, WI 53226, USA;2. Department of Radiology, Medical College of Wisconsin, 8701 Watertown Plk Rd., Milwaukee, WI 53226, USA;3. Center for Imaging Research, Medical College of Wisconsin, 8701 Watertown Plk Rd., Milwaukee, WI 53226, USA;1. Beijing City Key Lab for Medical Physics and Engineering, Institution of Heavy Ion Physics, School of Physics, Peking University, Beijing, China;2. Center for MRI Research, Peking University, Beijing, China;3. Department of Radiology, Beijing Tiantan Hospital, Capital Medical University, Beijing, China;4. Department of Radiology, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China;5. MR Research China, GE Healthcare, Beijing, China;6. State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China;7. McGovern Institute for Brain Research, Peking University, Beijing, China;8. Shenzhen Key Laboratory of Affective and Social Cognitive Science, Institute of Affective and Social Neuroscience, Shenzhen University, Shenzhen, China;9. Center for Emotion and Brain, Shenzhen Institute of Neuroscience, Shenzhen, China |
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| Abstract: | This paper focuses on modelling the severity distribution. We directly model the small, moderate and large losses with the Pareto Positive Stable (PPS) distribution and thus it is not necessary to fix a threshold for the tail behaviour. Estimation with the method of moments is straightforward. Properties, graphical tests and expressions for value-at risk and tail value-at-risk are presented. Furthermore, we show that the PPS distribution can be used to construct a statistical test for the Pareto distribution and to determine the threshold for the Pareto shape if required. An application to loss data is presented. We conclude that the PPS distribution can perform better than commonly used distributions when modelling a single loss distribution for moderate and large losses. This approach avoids the pitfalls of cut-off selection and it is very simple to implement for quantitative risk analysis. |
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