基于矩估计法的P范分布参数估计

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。

Parameter Estimation of P-norm Distribution Based on the Moments Approach

Parameter-estimation's accuracy of P-norm distribution have a great influence on estimate-efficiency of observations and the precision of data processing. In this paper, from the perspective of the actual situation of observations' distribution and simplifying operations, the two/four order moments estimation is introduced to estimate the shape parameter and variance, and the approximate formula of this method is given to calculate shape parameter. Another method based on logarithmic-expectation is introduced to further improve estimate efficiency, and the reasonable estimation expression of shape parameter p and variance σ is deduced by combining with the absolute and logarithmic-absolute moment. Finally, the simulated experiments are implemented to verify the correctness of the derived formula and proposed algorithm, and a comparison and analysis with the traditional maximum likelihood estimation method is made, it can be concluded that the two/four order moments estimation and logarithmic expectation moments estimation is better than maximum likelihood estimation in terms of convergence, stability and accuracy.