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

被引：6

作者：

Tomovski, Zivorad ^{[1
]}

Metzler, Ralf ^{[2
]}

Gerhold, Stefan ^{[3
]}

机构：

[1] Univ Ostrava, Fac Sci, Dept Math, 30 Dubna 22, Dubna 70103, Czech Republic

[2] Univ Potsdam, Inst Phys & Astron, Karl Liebknecht Str 24-25,Haus 28, D-14476 Potsdam, Germany

[3] TU Wien, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2022年 / 25卷 / 04期

关键词：

Fractional calculus (primary); Characteristic function; Mittag-Leffler function; Fractional moments; Mellin transform;

D O I：

10.1007/s13540-022-00047-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1307 / 1323

页数：17

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