On the fractional weibull process

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.

Automated summary

In this paper, the fractional Weibull process (fWp) is defined to address the limited engineering applications of the fractional Weibull distribution (fWd). The self-similarity property and long range dependence (LRD) are proven for fWp, and simulation using actual data validates the adaptability of fWd. The simulation is further expanded to the planar space by employing a random walk based on fWp.