On the fractional weibull process

Wujin Deng; Wanqing Song; Carlo Cattani; Jianxue Chen; Xiaolong Chen

doi:10.3389/fphy.2022.790791

Frontiers in Physics (Oct 2022)

On the fractional weibull process

Wujin Deng,
Wanqing Song,
Carlo Cattani,
Jianxue Chen,
Xiaolong Chen

Affiliations

Wujin Deng: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China
Wanqing Song: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China
Carlo Cattani: Engineering School, DEIM, University of Tuscia, Viterbo, Italy
Jianxue Chen: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China
Xiaolong Chen: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China

DOI: https://doi.org/10.3389/fphy.2022.790791
Journal volume & issue: Vol. 10

Abstract

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Engineering applications of the fractional Weibull distribution (fWd) are quite limited because a corresponding stochastic process is not yet constituted and completely analyzed of fundamental properties. In order to fill this gap, the fractional Weibull process (fWp) is defined in this paper with the realization algorithm. The self-similarity property as well as long range dependence (LRD) are proven for the future research. The simulation is conducted by the actual data. The fWd is utilized to fit the actual probability distribution and the corresponding process is generated to reflect the stochasticity of the data. The random walk based on the fWp expands the simulation to the planar space.

Published in Frontiers in Physics

ISSN: 2296-424X (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Science: Physics
Website: https://www.frontiersin.org/journals/physics

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