On the fractional weibull process

Abstract

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.

Heavy Tail and Long-Range Dependence for Skewed Time Series Prediction Based on a Fractional Weibull Process

“…We present 200 iterations of the fWp in Figure 2. The fWp is a stochastic process based on the fWd, and it thus presents skewed characteristics [6]. We present 200 iterations of the fWp in Figure 2.…”

“…The parameter estimation for the fWp is based on the maximum likelihood estimation in [6]. In this work, we present the estimation method for the drift and diffusion coefficients.…”

“…Long-range dependence is common among real stochastic time series [4,5]. The fractional Weibull process (fWp) is derived in [6] with respect to the fWd. The long-range dependence of the fWp is discussed in this work, so that the statistical prediction model can be established based on the fWp.…”