In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be ...
Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form ∫ $f_{1}(x)f_{2}(x-\theta )dx$, where ...
Copulas are functions that enable the construction of multivariate probability distributions by binding together univariate marginal distributions. Central to probability theory, they allow ...
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