Multimodal data are often present in synthetic aperture radar (SAR) image processing. Such images are often modeled by probability mixtures, but such solution may involve a large number of parameters and its inference becomes challenging. To address this issue, we proposed a probability distribution capable of describing multimodal data with only three parameters. The introduced model is defined by the sum of a random number, following the truncated Poisson law, of independent random variables with the Cauchy model, called compound truncated Poisson Cauchy (CTPC) distribution. We derived the characteristic function (cf), a distance measure between cfs, and provided estimators for the CTPC parameters: maximum likelihood estimators (MLEs) and quadratic distance estimators (QDEs). Furthermore, we derived a goodness-of-fit (GoF) distance based on the CTPC law and its empirical cf. To quantify the performance of the proposed estimators and GoF statistic, we employed a Monte Carlo simulation and the results suggest that QDEs outperform MLEs. Finally, we detail a numerical experiment with actual SAR data which describes a segment of SAR intensities with at least two types of textures. Our model could outperform six SAR intensities models: Weibull, gamma, generalized gamma, $\mathcal{K}$, ${\mathcal{G}}^0$, and beta generalized normal.

多模态数据通常出现在合成孔径雷达（SAR）图像处理中。这样的图像通常是通过概率混合来建模的，但是这样的解决方案可能涉及大量参数，并且其推断变得具有挑战性。为了解决这个问题，我们提出了一种概率分布，该概率分布能够仅使用三个参数来描述多峰数据。引入的模型由柯西模型由遵循截断的泊松定律的独立随机变量的随机数之和定义，称为复合截断的泊松·柯西（CTPC）分发。我们推导了特征函数（cf），cfs之间的距离度量，并提供了CTPC参数的估计器：最大似然估计器（MLE）和二次距离估计器（QDE）。此外，我们根据CTPC定律及其经验cf推导了拟合优度（GoF）距离。为了量化提议的估计量和GoF统计量的性能，我们采用了蒙特卡洛模拟，结果表明QDE的表现优于MLE。最后，我们用实际的SAR数据进行了一个数值实验，该实验描述了至少具有两种纹理的SAR强度段。我们的模型可以胜过六个SAR强度模型：Weibull，伽玛，广义伽玛，$\mathcal{ķ}$， ${\mathcal{G}}^0$和beta表示正常。