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首页> 外文期刊>International Journal of Statistics and Probability >The Bayes Premium in an Aggregate Loss Poisson-Lindley Model with Structure Function STSP
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The Bayes Premium in an Aggregate Loss Poisson-Lindley Model with Structure Function STSP

机译：贝叶斯溢价在汇总泊松 - 林德利模型，结构功能STSP

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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 $heta_{1}$ in $[0,1]$, which is a potential alternative to describe these situations. As the structure function for $heta_{1}$ 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.
机译：精算科学中的许多溢价计算问题考虑声称的数量，表示为k，作为可变风险。传统上，这种随机变量由泊松分布建模。然而，众所周知，汽车保险组合的特征在于零充气（样本中的零值的高百分比）和过度分散（方差大于平均值），以及？泊松分布没有正确反映最后一个现象。在本文中，我们考虑到ke inst-lindley分布，k = theta_ {1} $ in $ [0,1] $的潜在替代方案来确定贝斯普罗斯级别，这是描述这些情况的潜在替代方案。作为$ theta_ {1} $的结构函数我们引发标准化？双面配电，这是一种合理的替代方案，对通常的β发行。此外，通过Poisson-Lindley分布给出的主要分布，考虑了总损失模型。开发了贝叶斯分析以获得贝叶斯溢价。结论是，STSP在问题的问题中不是一个充分的替代方案，因为它比β发行更具信息丰富，而且分散。

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