2017/06/05 by Roberto Fontana, Fontana, Roberto, Patrizia Semeraro +1
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Control Systems and Identification #Diverse Scientific and Engineering Research #FOS: Mathematics #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1706.01357
openalex publication_date 2017/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We express each Fr 'echet class of multivariate Bernoulli distributions with\ngiven margins as the convex hull of a set of densities, which belong to the\nsame Fr 'echet class. This characterisation allows us to establish whether a\ngiven correlation matrix is compatible with the assigned margins and, if it is,\nto easily construct one of the corresponding joint densities. % Such\n%representation is based on a polynomial expression of the distributions of a\nFr 'echet class. We reduce the problem of finding a density belonging to a\nFr 'echet class and with given correlation matrix to the solution of a linear\nsystem of equations. Our methodology also provides the bounds that each\ncorrelation must satisfy to be compatible with the assigned margins. An\nalgorithm and its use in some examples is shown.\n