Positive-part moments via characteristic functions, and more general expressions

© 2016, Springer Science+Business Media New York. A unifying and generalizing approach to representations of the positive-part and absolute moments EX+p and E| X| p of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of X+, generalized moments EX+peiuX, truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed