基于矩估计法的P范分布参数估计

发布时间：2018-03-16 23:10

本文选题：P范分布　切入点：参数估计　出处：《武汉大学学报(信息科学版)》2017年04期 　论文类型：期刊论文

【摘要】：P范分布的参数估计值的精度对观测值的估计效率和数据处理的精度影响较大。从观测值分布的实际情况和简化运算出发,引入二/四阶矩估计方法估计P范分布的形状参数和方差,给出了二/四阶矩估计法的形状参数的近似计算式。为了进一步提高估计效率,引入对数期望矩估计法,将绝对矩与对数绝对矩相结合,导出了基于对数期望矩估计法的P范分布形状参数p、方差σ的合理估计表达式。最后利用两组模拟数据对该模型和计算方法的正确性进行了验证,并与传统极大似然估计方法进行了对比分析。结果表明,当样本数较少时,二/四阶矩估计法和对数期望矩估计法在收敛性、稳定性和准确性等方面优于极大似然估计法。
[Abstract]:The precision of parameter estimation of P-norm distribution has a great influence on the efficiency of estimation and the precision of data processing. The second / fourth order moment estimation method is introduced to estimate the shape parameter and variance of P-norm distribution, and the approximate formula of shape parameter of the second / fourth order moment estimation method is given. In order to further improve the estimation efficiency, the logarithmic expected moment estimation method is introduced. Combining absolute moments with logarithmic absolute moments, A reasonable estimate expression of shape parameter p, variance 蟽 of P-norm distribution based on the method of estimating expected moment is derived. At last, the correctness of the model and calculation method is verified by two sets of simulation data. The results show that the second / fourth order moment estimation method and the logarithmic expected moment estimation method are superior to the maximum likelihood estimation method in convergence, stability and accuracy when the number of samples is small.
【作者单位】：中国地质大学(武汉)信息工程学院;中铁工程设计咨询集团有限公司;国网电力科学研究院武汉南瑞有限责任公司;
【基金】：国家自然科学基金(41374017,40974002,11471105)~~
【分类号】：P207

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