期刊名称：International Journal of Statistics and Probability
印刷版ISSN：1927-7032
电子版ISSN：1927-7040
出版年度：2013
卷号：2
期号：2
页码：47
DOI：10.5539/ijsp.v2n2p47
出版社：Canadian Center of Science and Education
摘要：Many premium calculating problems in actuarial science consider the number of claims, denoted as K, as the variable risk. Traditionally, this random variable is modelled by the Poisson distribution. However, it is well known that automobile insurance portfolios are characterized by zero-inflation (high percentage of zero values in the sample) and overdispersion (the variance is greater than the mean), and the Poisson distribution does not properly reflect the last phenomenon. In this paper we determine the Bayes premium considering that K follows a Poisson-Lindley distribution, with parameter $\theta_{1}$ in $[0,1]$, which is a potential alternative to describe these situations. As the structure function for $\theta_{1}$ we elicit the standardized two-sided power distribution, which is a reasonable alternative to the usual beta distribution. In addition, an aggregate loss model is considered with primary distribution given by the Poisson-Lindley distribution. A Bayesian analysis is developed to obtain the Bayes premium. The conclusion is that the STSP is not an adequate alternative in the problem in question because it is more informative and less dispersed than the Beta distribution.
