Further Applications of D-Norms to Probability & Statistics
This section introduces max-characteristic functions (max-CFs), which are an offspring of D-norms. A max-CF characterizes the distribution of an rv in \(\mathbb R^d\), whose components are non-negative and have finite expectation. Pointwise convergence of a max-CF is shown to be equivalent to convergence with respect to the Wasserstein metric. An inversion formula for max-CF is established as well.
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