We focus on some statistical facets of the Riesz probability distribution that could replace and exceed the Wishart in many application fields. First, the maximum likelihood (ML) estimators of both Riesz parameters are derived using two approaches. The first one yields an equation solved using an algorithm alternating the Cholesky decomposition with intermediate calculations. The second one provides a closed-form solution of the ML-estimator, which is proven to be asymptotically unbiased. Afterward, we assume a Riesz as a prior for the maximum a posteriori estimator (MAP) of the scale parameter, which heads to a Riesz Inverse Gaussian ($\mathcal{R}\mathcal{I}\mathcal{G}$) posterior distribution. The resulting MAP estimator is simplified and solved via an algorithm alternating the Denman-Beavers algorithm and the Cholesky decomposition. We also characterize the Riesz-$\mathcal{R}\mathcal{I}\mathcal{G}$ model uniquely by a conditional distribution and a regression assumption. Finally, some supporting simulations illustrate the efficiency of these estimators. The corresponding computer codes are provided.

我们专注于 Riesz 概率分布的一些统计方面，这些方面可以在许多应用领域取代和超越 Wishart。首先，使用两种方法导出两个 Riesz 参数的最大似然 (ML) 估计量。第一个产生一个方程，使用一种算法将 Cholesky 分解与中间计算交替进行求解。第二个提供了 ML 估计器的封闭形式的解决方案，它被证明是渐近无偏的。之后，我们假设 Riesz 作为尺度参数的最大后验估计量 (MAP) 的先验，它指向 Riesz 逆高斯 ($\mathcal{电阻}\mathcal{一世}\mathcal{G}$) 后验分布。通过交替使用 Denman-Beavers 算法和 Cholesky 分解的算法来简化和求解所得 MAP 估计量。我们还描述了 Riesz-$\mathcal{电阻}\mathcal{一世}\mathcal{G}$通过条件分布和回归假设唯一地建模。最后，一些支持模拟说明了这些估计器的效率。提供相应的计算机代码。