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.