一元P-范分布参数估计的改进方法

An improvement method of parameters estimation in P-norm distribution

当观测误差服从P范分布时,本文从P范分布的概率密度函数和统计性质出发,利用绝对矩得到了参数p和方差的合理选择公式,给出了一种P范分布的参数的估计方法,可以使误差分布更加接近真实分布。将得到的参数估值作为应用极大似然估计法进行迭代时的初值,从而减少了运算时间,提高了运算效率。同时,将模型展开为泰勒级数,取至二次项,从而使线性近似引起的模型误差达到最小,提高了估值结果的精度。最后用两个模拟算例对本文的方法加以验证。

The P-norm distribution is an extensive distribution family of measuring errors.For each concrete measuring data,a suitable value for P could be selected to make the theoretical model of the error distribution be more close to the real one of the error than the normal distribution,which was used in data processing.In this paper,a fast parameter estimation of P-norm distribution was brought forward.The method of fast parameter estimation and the maximum likelihood adjustment were combined to calculate parameter.Two examples were presented finally,the new method presented in this paper showed an effective way of solving the problem,and the estimated values were nearer to their theoretical ones than the moment method of estimation or the maximum likelihood adjustment.