拖尾Rayleigh 分布: 基本性质及其应用

针对使用拖尾Rayleigh分布对合成孔径雷达(Synthetic aperture radar, SAR)幅值图像建模时遇到的问题, 本文讨论了拖尾Rayleigh分布的相关性质及其应用. 首先, 基于负数阶矩理论, 本文提出了拖尾Rayleigh分布的比值估计、对数矩估计和迭代对数矩估计三种参数估计方法, 并通过Monte Carlo仿真实验比较了它们的估计性能. 其次, 本文使用渐近级数计算拖尾Rayleigh分布的概率密度函数, 基于插值多项式拟合, 提出了高效计算密度函数的三步方法. 最后, 本文给出了SAR幅值图像基于拖尾Rayleigh分布的建模实例. 结果表明, 和一般的Rayleigh分布相比, 拖尾Rayleigh分布可以精确反映SAR幅值图像尖峰厚尾的统计特征, 因此它是SAR幅值图像建模的有效工具.

Heavy-tailed Rayleigh Distribution: Basic Properties and Their Applications

In order to solve the problems appearing in the heavy-tailed Rayleigh modeling of synthetic aperture radar (SAR)amplitude images,some basic properties and their applications are introduced for the heavy-tailed Rayleigh dis- tribution in this paper.Firstly,based on the negative-order moments,ratio method,logarithmic moment method and iterative logarithmic moment method are presented to estimate the parameters of the heavy-tailed Rayleigh distribution, and their performances are compared according to Monte Carlo simulations.Secondly,the asymptotic series are used to evaluate the density function of heavy-tailed Rayleigh distribution,and an efficient three-step method is proposed using the interpolating polynomial fit.Lastly,real SAR amplitude images are modeled with the heavy-tailed Rayleigh distribution.Compared to the conventional Rayleigh distribution,the heavy-tailed Rayleigh distribution can accurately reflect the high peak and heavy tail of SAR amplitude images,so it is a useful tool for the modeling of SAR amplitude images.