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

TITLE=On the fractional weibull process

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.790791

DOI=10.3389/fphy.2022.790791

ISSN=2296-424X

ABSTRACT=<p>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.</p>