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A Sarmanov family with beta and gamma marginal distributions: an application to the Bayes premium in a collective risk model

机译：一个具有beta和gamma边际分布的Sarmanov家庭：在集体风险模型中对Bayes溢价的应用

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摘要

In this paper we firstly develop a Sarmanov-Lee bivariate family of distributions with the beta and gamma as marginal distributions. We obtain the linear correlation coefficient showing that, although it is not a strong family of correlation, it can be greater than the value of this coefficient in the Farlie-Gumbel-Morgenstern family. We also determine other measures for this family: the coefficient of median concordance and the relative entropy, which are analyzed by comparison with the case of independence. Secondly, we consider the problem of premium calculation in a Poisson-Lindley and exponential collective risk model, where the Sarmanov-Lee family is used as a structure function. We determine the collective and Bayes premiums whose values are analyzed when independence and dependence between the risk profiles are considered, obtaining that notable variations in premiums values are obtained even when low levels of correlation are considered.
机译：在本文中，我们首先建立一个以β和γ为边际分布的Sarmanov-Lee二元分布族。我们获得的线性相关系数表明，尽管它不是一个强大的相关族，但它可以大于Farlie-Gumbel-Morgenstern族中该系数的值。我们还为这个家庭确定了其他度量：中位数一致性系数和相对熵，通过与独立性案例进行比较来分析。其次，我们考虑在Poisson-Lindley和指数集体风险模型中计算保费的问题，其中Sarmanov-Lee家族用作结构函数。当确定风险分布之间的独立性和依赖性时，我们确定了将对其价值进行分析的集体保费和贝叶斯保费，从而获得了即使在考虑低相关性的情况下也可获得保费价值的显着变化。

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