A framework defines weak moments, cumulants, and a central limit theorem for probability laws lacking classical moments by representing laws as tempered distributions probed by a Schwartz kernel.
Schwartz (1950–1951).Th´ eorie des distributions
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Distributional Statistical Models: Weak Moments, Cumulants, and a Central Limit Theorem
A framework defines weak moments, cumulants, and a central limit theorem for probability laws lacking classical moments by representing laws as tempered distributions probed by a Schwartz kernel.