Formulas of Absolute Moments

Gwo Dong Lin () and Chin-Yuan Hu ()
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Gwo Dong Lin: Hwa-Kang Xing-Ye Foundation
Chin-Yuan Hu: National Changhua University of Education

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 20, 476-495

Abstract: Abstract The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat Hsu’s (J. Chinese Math. Soc. N.S. 1, 257–280, 1951) formulas in terms of the characteristic function (which have been ignored in the literature) and provide some new results as well. The case of nonnegative random variables is also investigated through both characteristic function and Laplace–Stieltjes transform. Besides, we prove that the distribution of a nonnegative random variable with a finite fractional moment can be completely determined by a proper subset of the translated fractional moments. This improves significantly Hall’s (Z. Wahrsch. Verw. Gebiete 62, 355–359, 1983) result for distributions on the right half-line.

Keywords: Absolute moments; Fractional moments; Translated moments; Characteristic function; Fourier–Stieltjes transform; Laplace–Stieltjes transform; Ramanujan’s master theorem; Primary 60E10; 42A38; 42B10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-019-00196-x

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