基于负数阶矩的正值Alpha稳定分布的参数估计

为了精确估计正值alpha稳定（PAS）分布的参数，基于负数阶矩理论，提出了比值估计、对数矩估计和迭代对数矩估计3种参数估计方法．比值估计直接利用特定阶次的负数阶矩的比值来估计未知参数，对数矩估计利用PAS分布的对数变换及其负数阶矩的Taylor展式从而获得解析的估计形式，迭代对数矩估计通过样本分段迭代估计未知参数．与传统的估计方法相比，所提出的3种估计方法可以获得更高的估计精度，并且对数矩估计具有较低的计算复杂度．MonteCarlo仿真实验表明，当独立运行次数为100、样本总数为5000时，比值估计的估计精度可以达到99．8％，对数矩估计的估计精度可以达到99．95％，迭代对数矩估计的估计精度可以达到99．94％．

Positive Alpha-Stable Distributed Parameter Estimation Based on Negative-Order Moments

In order to accurately estimate the positive alpha-stable(PAS) distributed parameters,three kinds of parameter estimate methods,namely ratio,logarithmic moment and iterative logarithmic moment estimate are proposed based on negative-order moments.Ratio of the negative-order moments is directly used for the ratio estimation,and the logarithmic transformation of PAS distribution and Taylor series of the negative-order moment are used to obtain an analytical form of logarithmic moment estimation.Through dividing all samples into different segments,the iterative logarithmic moment estimation is obtained according to iterative computation of data segments.Compared to the conventional estimates,these three estimates achieve much higher estimation accuracy,and the logarithmic moment estimator has lower computing complexity.Monte Carlo simulation results demonstrate that the estimation accuracy of these three estimations can reach 99.8%,99.95%,and 99.94% respectively when the independent running times are 100 and the number of all samples is 5 000.