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The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics

机译:Rician高斯逆分布:非瑞利信号幅度统计的新模型

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In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral /spl chi//sup 2/-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.
机译:在本文中,我们介绍了一种用于建模非瑞利幅度统计的新统计分布,我们将其称为Rician逆高斯(RiIG)分布。它是莱斯分布和高斯逆分布的混合。概率密度函数(pdf)以封闭形式作为三个参数的函数给出。从某种意义上说,它可以适应各种形状,从瑞利形pdf到非中心/ spl chi // sup 2 /形pdf,它使pdf非常灵活。对该新模型的理论基础进行了相当详尽的讨论,并且我们还给出了两种迭代算法来从数据中估计其参数。最后,我们提供了一些建模示例,我们在其中测试了分布表示线性医疗超声数据和单视场合成孔径雷达数据的区域幅度直方图的能力。我们将RiIG模型与K模型的拟合优度进行了比较,并且在大多数情况下,新模型被证明是一种更好的数据统计模型。我们还包括一系列对数似然检验,以评估所提出模型的预测性能。

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