Synthesis Weibull Stochastic Differential Equation: Properties and application

Abstract

The Weibull distribution is suitable for modeling stochastic phenomena. However, most of the existing stochastic differential equations (SDEs) of Weibull type found in the literature do not follow the Weibull distribution, making them unsuitable for modeling phenomena that follow a Weibull random variable. To address this issue, this paper proposes a new SDE known as the Synthesis Weibull Stochastic Differential Equation (SWSDE) using the synthesis method. Some properties and numerical studies were carried out. The usefulness of the model is also demonstrated using Malawian wind speed data. The results show that the proposed SDE is suitable for predicting the data. The model also demonstrates a mean-reverting property, whereby the equilibrium is the solution of a differential equation in simulation studies. Additionally, the solutions of the model are found to always follow the Weibull distribution.