负二项分布的优良特性及其在风险管理中的应用

孟生旺．负二项分布的优良特性及其在风险管理中的应用．数理统计与管理，１９９８，１７（２），９～１２．负二项分布之所以在风险管理中被广泛应用是由其优良特性所决定的。本文主要讨论了其中三个方面的问题：第一，负二项分布在描述风险集体中任意风险的索赔次数时表现为伽玛分布对泊松分布按参数变化的加权平均；第二，负二项分布在描述某些风险的累积索赔额时具有复合泊松分布的形式；第三，负二项分布是当风险的索赔频率强度之间存在正向传染时索赔次数的分布

Properties of Negative Binomial Distribution and It′s Application to Risk Management

egative-binomial distribution has been widely used in risk management because of its good properties. This paper concentrates mainly on three of these properties:First, it is a weighted Poisson distribution with weights as being Gamma distributed when used to describe the distribution of claim numbers of a risk in the collective. Next, it has a form of compound Poisson distribution when claim amount is Logrithmic. Finally, when claim frequency intensities have positive contagion, the claim number distribution is negativebinomial.