A unified expression of Gompertz and logistic curves and its discretization

In this study, we newly propose a generalized growth curve model of discrete type, which is based on the property of the Gompertz and logistic curve models. In particular, the bi-linearization technique is applied to the basic differential equation, and we discretize it to the difference equations so as to hold the property of integrable systems. These models can be used to predict the future behavior of the time series data by estimating the constant parameters included in the model. In the numerical examples, we analyze the actual data sets by using our model, and also we show the confidence intervals of the estimated growth curve via the bootstrap method.