Fractional characteristic functions, and a fractional calculus approach for moments of random variables

被引：0
作者：
Živorad Tomovski
Ralf Metzler
Stefan Gerhold
机构：
[1] University of Ostrava,Department of Mathematics, Faculty of Sciences
[2] University of Potsdam,Institute of Physics and Astronomy
[3] TU Wien,undefined
来源：
Fractional Calculus and Applied Analysis | 2022年 / 25卷
关键词：
Fractional calculus (primary); Characteristic function; Mittag–Leffler function; Fractional moments; Mellin transform; 60E10; 26A33; 33E12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is uniformly continuous. We show that fractional moments can be expressed in terms of Riemann–Liouville integrals and derivatives of the fractional characteristic function. The fractional moments are of interest in particular for distributions whose integer moments do not exist. Some illustrative examples for particular distributions are also presented.
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页码：1307 / 1323
页数：16
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