Fractional characteristic functions, and a fractional calculus approach for moments of random variables
- 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.
| Author details: | Živorad TomovskiGND, Ralf MetzlerORCiDGND, Stefan GerholdORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s13540-022-00047-x |
| ISSN: | 1314-2224 |
| Title of parent work (English): | Fractional calculus and applied analysis : an international journal for theory and applications |
| Publisher: | De Gruyter |
| Place of publishing: | Berlin ; Boston |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/06/15 |
| Publication year: | 2022 |
| Release date: | 2024/01/25 |
| Tag: | Characteristic function; Fractional calculus (primary); Fractional moments; Mellin transform; Mittag-Leffler; function |
| Volume: | 25 |
| Issue: | 4 |
| Number of pages: | 17 |
| First page: | 1307 |
| Last Page: | 1323 |
| Funding institution: | German Science Foundation (DFG) [ME 1535/12-1]; DAAD foundation |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Hybrid Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
