对称稳定分布的对数累积量参数估计

Log-cumulant parameter estimator of symmetric stable distribution

基于第二类统计量,提出了估计对称稳定分布参数的有效方法。对累积分布函数求导数,获得对称稳定分布的绝对值的概率密度函数;对对称稳定分布的绝对值进行Mellin变换,推导出对称稳定分布的绝对值的第二类第一特征函数。由第二类第一特征函数推导出对称稳定分布的绝对值的前两阶对数累积量,可以估计对称稳定分布的参数。对数累积量估计拥有简洁的估计式,便于实现。参数估计实验结果表明,和传统的估计方法相比,该方法具有较高的估计性能,是对称稳定分布的高效参数估计方法。

Based on the second-kind statistics, an effective parameter estimator is proposed for the symmetric stable distribution. Taking the derivative on the cumulative distribution function, the probability density function of the absolute value of symmetric stable distribution is obtained firstly. Second, the Mellin tranSformation of the absolute value of symmetric stable distribution is employed, and the second-kind first characteristic function of the absolute value of symmetric stable distribution is derived. Last, the first two log-cumulants of the absolute value of symmetric stable distribution are derived from the second-kind first characteristic function for parameter estimation of symmetric stable distribution. With the compact estimation expressions, the log-cumulant estimator is easy to implement. Parameter estimation experiments demonstrate that, compared to the traditional estimators, the proposed estimator owns higher estimation performance, so it is the efficient parameter estimator of the symmetric stable distribution.