Abstract
We introduce a method for modelling a continuous response which is the sum of a random number of terms. Examples are total insurance claim sizes (the total of all claims on a policy in a year), or total amount spent by credit card holders in a sector in a month, where there may be multiple spending episodes. The distribution of the number of terms may be, in principle, any discrete distribution defined on the non-negative integers; and each term has a continuous, right-skewed distribution. The resulting marginal distribution of the total amount is a mixed discrete-continuous model, with a probability mass at zero and a continuous component. The model explicitly specifies log-linear models for the four parameters in the total amount distribution. It may be fitted to data using a package written in R. The method is illustrated on an Australian motor vehicle insurance data set.
Original language | English |
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Title of host publication | Proceedings of the 22nd International Workshop on Statistical Modelling |
Editors | Joan del Castillo, Anna Espinal, Pere Puig |
Place of Publication | Barcelona, Spain |
Publisher | L'Institut d'Estadistica de Catalunya, IDESCAT |
Pages | 323-328 |
Number of pages | 6 |
ISBN (Print) | 9788469059432 |
Publication status | Published - 2007 |
Event | International Workshop on Statistical Modelling (22nd : 2007) - Barcelona, Spain Duration: 2 Jul 2007 → 6 Jul 2007 |
Workshop
Workshop | International Workshop on Statistical Modelling (22nd : 2007) |
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City | Barcelona, Spain |
Period | 2/07/07 → 6/07/07 |
Keywords
- mixture distribution
- mean and dispersion modelling
- insurance claims
- compound Poisson
- discrete mixture