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Abstrakty
The concept of a mixture of distributions is an important one in insurance, since insurance companies generally deal with heterogeneous risks. The simplest model for the number of claims is the Poisson model, so we assume that the number of claims Ni made by policyholder i follows the Poisson distribution with mean λi. We know that the values of λi will vary across the portfolio. We take distribution gamma as the mixing distribution for the Poisson means and show that the marginal distribution of the number of claims is negative binomial. In second example we suppose that each individual in a large insurance portfolio incurs losses according to its own exponential distribution, i.e. the exponential distributions have means which differ from individual to individual. Our purpose is to describe the losses over the whole portfolio. We show that the mixture distribution is Pareto when exponentially distributed losses are averaged using a gamma mixing distribution. (fragment of text)
Rocznik
Strony
41--44
Opis fizyczny
Twórcy
autor
- University of Economics in Bratislava, Slovakia
Bibliografia
- Currie I.D.: Loss Distributions. Institute of Actuaries and Faculty of Actuaries, London and Edinburgh, 1993.
- Dickson D.C.M., Waters H.R.: Risk models. Institute of Actuaries and Faculty of Actuaries, London and Edinburgh, 1993.
- Hogg, R.V., Klugman S.A.: Loss Distributions. John Wiley & Sons, New York, 1984.
- Pacáková V.: Štatistika pre poistnú prax. STATIS Bratislava, 1999.
- Pacáková V.: Mixture Distributions and Variability in a Heterogeneous Portfolio of Policies. Proceedings of the Seminar Statistical Methods in Socioeconomic Researches - Theory and Applications, Krakow 2000.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171385525