- - - College of Administration and Economics, University of Al-Hamdaniya, Iraq
- - - College of Administration and Economics, University of Bagdad, Iraq

Some properties of the geometric stochastic process (GSP) are studied along with those of a related process which we propose to call the Double geometric stochastic process (DGSP), under certain conditions. This process also has the same advantages of tractability as the geometric stochastic process; it exhibits some properties which may make it a useful complement to the multiple Trends geometric stochastic process. Also, it may be fit to observed data as easily as the geometric stochastic process. As a first attempt, the proposed model was applied to model the data and the Coronavirus epidemic in Iraq to reach the best model that represents the data under study. A chicken swarm optimization algorithm is proposed to choose the best model representing the data, in addition to estimating the parameters a, b, \(\mu\), and \(\sigma^{۲}\) of the double geometric stochastic process, where \(\mu\) and \(\sigma^{۲}\) are the mean and variance of \(X_{۱}\), respectively.

double geometric stochastic process, geometric stochastic process, Parameter estimation, chicken swarm optimization algorithm, multiple monotone trends, root mean square criteria