Gompertz Stochastic Differential Equation growth model with discrete delay: application in forecasting all India marine and inland fish production

Abstract

The present study considered the well-known Gompertz growth model. The effect of random environmental fluctuations in the parameters is modelled employing Stochastic Differential Equation (SDE) approach. Importance of incorporating discrete delay in this model is highlighted. The methodology for fitting the resultant model in terms of Stochastic Delay Differential Equation (SDDE) is described. Relevant computer program for fitting Gompertz SDDE (GSDDE) model is written in SAS package. Finally, as an illustration, superiority of GSDDE model over Gompertz SDE (GSDE) model for fitting and forecasting purposes is shown for all India marine and inland catch data sets.