P范分布的实数阶与对数矩估计法

doi:10.11947/j.AGCS.2016.20150166

测绘学报 ›› 2016, Vol. 45 ›› Issue (3): 302-309.doi: 10.11947/j.AGCS.2016.20150166

P范分布的实数阶与对数矩估计法

潘雄, 罗静, 汪耀

中国地质大学信息工程学院, 湖北武汉 430074

收稿日期:2015-03-30 修回日期:2015-11-04 出版日期:2016-03-20 发布日期:2016-03-25
作者简介:潘雄(1973-),男,博士后,教授,研究方向为测量数据处理的理论及应用。
基金资助:
国家自然科学基金(41374017;40974002;11471105);国家博士后基金(2005038362)

Real Order and Logarithmic Moment Estimation Method of P-norm Distribution

PAN Xiong, LUO Jing, WANG Yao

Faculty of Information Engineering, China University of Geosciences, Wuhan 430074, China

Received:2015-03-30 Revised:2015-11-04 Online:2016-03-20 Published:2016-03-25
Supported by:
The National Natural Science Foundation of China(Nos.41374017;40974002;11471105);The China Postdoctoral Science Foundation(No.2005038362)

摘要/Abstract

摘要： 从参数估计的精度和算法的复杂度出发,对P范分布参数的估计方法进行了改进。根据误差分布的实际情况,引入实数阶和对数矩估计方法,建立了P范分布的参数估计的实数阶矩估计方法。首先,利用实数阶矩估计法,导出了形状参数p与实数阶阶数r的关系式,对形状参数的选取给出了相应的建议;其次,改进矩估计理论,利用对数矩估计方法导出了形状参数、期望及中误差的非线性估计公式,消除了函数截断误差对参数估计值计算的影响,并利用迭代算法给出了相应参数的解算方法和计算流程;最后,用一个模拟算例和两个实测算例分析了实数矩、对数矩和极大似然估计3种估计方法的稳定性和精度。结果说明,本文提出的矩估计方法在稳定性、精度和收敛速度等方面均优于极大似然估计方法,推广了现有的误差理论。

关键词: P范分布, 矩估计法, 参数估计

Abstract: The estimation methods of P-norm distribution is improved in this paper from the perspective of the parameters estimation precision and algorithm complexity. The real order and logarithmic moment estimation is introduced and the real order moment estimation method of P-norm distribution is established based on the actual error distribution. First of all, the relation between the shape parameter p and the real order value r is derived by using the real order moment estimation, and corresponding suggestions are provided for shape parameter's selection. Then, the nonlinear estimation formula of shape parameter, expectations and mean square error is derived via logarithmic moment estimation, function truncation error on the calculation of parameter estimation is eliminated and the solving method of corresponding parameters and calculation process is given, leading an improvement of the theory. Finally, some examples are performed for analyzing the stability and precision of such three methods including real order moment, logarithmic moment and maximum likelihood estimation. The result shows that the stability, precision and convergence speed of the method in this paper are better than maximum likelihood estimation, which generalized the existing errors theory.

Key words: P-norm distribution, moment estimation, parameter estimation

中图分类号:

P207

潘雄, 罗静, 汪耀. P范分布的实数阶与对数矩估计法[J]. 测绘学报, 2016, 45(3): 302-309.

PAN Xiong, LUO Jing, WANG Yao. Real Order and Logarithmic Moment Estimation Method of P-norm Distribution[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(3): 302-309.

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P范分布的实数阶与对数矩估计法

Real Order and Logarithmic Moment Estimation Method of P-norm Distribution

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