标题： 具有指定边缘的多元伯努利分布的特征化 显示英文标题

标题： Characterization of multivariate Bernoulli distributions with given margins

摘要： 我们将具有指定边缘分布的多元伯努利分布的每个弗雷歇类表示为一组密度函数的凸包，这些密度函数属于同一弗雷歇类。 这种刻画使得我们可以判断一个给定的相关矩阵是否与指定的边缘分布兼容，并且如果兼容的话，可以轻松构造相应的联合密度函数之一。 我们把寻找属于某个弗雷歇类且具有指定相关矩阵的密度的问题转化为求解一个线性方程组。 我们的方法还给出了每个相关系数必须满足的界限，以确保其与指定的边缘分布兼容。 展示了一个算法及其在一些例子中的应用。 显示英文摘要

摘要： We express each Fr\'echet class of multivariate Bernoulli distributions with given margins as the convex hull of a set of densities, which belong to the same Fr\'echet class. This characterisation allows us to establish whether a given correlation matrix is compatible with the assigned margins and, if it is, to easily construct one of the corresponding joint densities. % Such %representation is based on a polynomial expression of the distributions of a Fr\'echet class. We reduce the problem of finding a density belonging to a Fr\'echet class and with given correlation matrix to the solution of a linear system of equations. Our methodology also provides the bounds that each correlation must satisfy to be compatible with the assigned margins. An algorithm and its use in some examples is shown.