采用梅林变换的帕累托分布参数估计方法

Estimation of parameters of Pareto distribution using Mellin transform

传统的海杂波帕累托分布模型参数估计方法存在估计范围受限,计算复杂,受脉冲积累个数限制等问题.针对上述问题,提出一种新的形状参数估计方法.首先对海杂波帕累托分布模型的概率密度函数进行梅林变换;然后分别计算了不同脉冲积累个数时帕累托分布的第二类特征函数,详细推导了帕累托分布的前两阶对数累积量;最后通过蒙特卡罗仿真实验将所提方法与现有方法的性能进行了对比.结果表明,所提出的方法与最大似然估计法相比具有更为简洁的解析表达式,与传统矩估计法相比,可以估计所有定义域内的形状参数,且不受脉冲积累个数限制.大量仿真实验证明,所提方法可将传统方法的相对偏差降低至少90%.

Some traditional parameters estimation methods have some problems that the estimation range is limited,that the computation is complicated,and that the number of pulses accumulated is limited.In order to solve these problems,a novel parameter estimation method of sea clutter under Pareto distribution is proposed in this paper.In the proposed method,the probability density function is firstly transformed with Mellin transform.Then the second kind of characteristic function of Pareto distribution is computed under the different numbers of pulses,and the first two logarithmic cumulants of Pareto distribution are deduced in detail.Finally,a comparison between the proposed method and some traditional methods is made based on the Monte Carlo simulation experiments.Experimental results show that the proposed method not only can estimate the parameters in all defined domains with a high fitting precision,but also has a more concise analytical expression with a low computational complexity.