论文标题
混合泊松随机总和的收敛和推断
Convergence and inference for mixed Poisson random sums
论文作者
论文摘要
在本文中，我们获得了一类混合泊松分布后的部分总和的限制分布。最终的极限是正态分布和指数族之间的混合，我们由正常指数族（NEF）定律称呼。引入了一个新的稳定概念，并建立了α稳定分布与NEF定律之间的关系。我们通过矩的方法以及最大似然法提出了NEF模型参数的估计，该方法是通过期望最大化算法进行的。介绍了蒙特卡洛模拟研究，以检查拟议估计量的性能，并提出了金融市场的经验说明。
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family, which we call by normal exponential family (NEF) laws. A new stability concept is introduced and a relationship between α-stable distributions and NEF laws is established. We propose estimation of the parameters of the NEF models through the method of moments and also by the maximum likelihood method, which is performed via an Expectation-Maximization algorithm. Monte Carlo simulation studies are addressed to check the performance of the proposed estimators and an empirical illustration on financial market is presented.
