Parameter Interval Estimation for Yule-Simon Distribution

尤尔分布中参数的区间估计

Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.

尤尔分布在网络科学、生物学和人文科学中有着广泛的应用.相关的研究工作主要集中在经验数据与尤尔分布的拟合程度分析或参数估计问题,所以仍存在一些尚未解决的问题,比如参数估计的误差分析,参数极大似然估计的迭代算法收敛性的理论证明等.尤尔分布是一个重尾分布,在很多应用场合,该分布的参数小于2从而导致方差不存在,这使得参数的区间估计的构建存在一些困难.利用压缩变换,本文给出了一种基于中心极限定理的区间估计方法。该方法适用于许多重尾分布的区间估计.另外,本文还基于最大似然法和众数方法,分别得到了参数的渐近置信区间.文中通过模拟计算和实际数据分析,对这三种区间估计方法进行了比较.