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| Content Provider | Springer Nature Link |
|---|---|
| Author | Zocher, Mathias |
| Copyright Year | 2005 |
| Abstract | In diesem Artikel wird der Weg von einem univariaten gemischten Poisson–Prozess, der in vielen Bereichen zum Zählen von Ereignissen benutzt wird, zu einem bivariaten gemischten Poisson–Prozess aufgezeigt. Dazu werden einige Eigenschaften des bivariaten Prozesses angegeben. Im zweiten Teil der Arbeit wird gezeigt, wie mit Hilfe dieses Prozesses der Übergang von einem herkömmlichen Bonus–Malus–System in der Kraftfahrthaftpflichtversicherung zu einem Bonus–Malus–System mit Berücksichtigung der Schadenart beschritten werden kann. Dazu wird zuerst eine Modellprüfung der gegebenen Daten vorgenommen und sodann werden für verschiedene mischende Verteilungen die Verteilungsparameter geschätzt und Nettoprämien angegeben sowie die Prognosegenauigkeit getestet.In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus–malus system handling different types of accidents can be derived from the classical bonus–malus system in third–party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities. |
| Starting Page | 383 |
| Ending Page | 402 |
| Page Count | 20 |
| File Format | |
| ISSN | 00026018 |
| Journal | AStA Advances in Statistical Analysis |
| Volume Number | 89 |
| Issue Number | 4 |
| e-ISSN | 16140176 |
| Language | German |
| Publisher | Springer-Verlag |
| Publisher Date | 2005-01-01 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | Subscribed |
| Subject Keyword | Bivariate mixed Poisson process bonus–malus–system multinomial property net premium prediction JEL C53 G22 Probability Theory and Stochastic Processes Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Econometrics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics and Probability |
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