Moments by Integrating the Moment-Generating Function (opens in new tab)

arXiv:2410.23587v5 Announce Type: replace-cross Abstract: We introduce a general integral framework for computing fractional, complex, absolute, and logarithmic moments from the moment-generating function (MGF) under explicit regularity conditions. By evaluating a complex extension of the MGF along a vertical contour, we obtain exact integral expressions that bypass the need for explicit probability densities and high-order derivatives. We establish conditions for negative fractional moments ...