In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the \(d_2\)-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

在本文中，我们提出了一个灵活的增长模型，该模型构成了著名的Gompertz模型的适当概括。我们对感兴趣的各种功能进行分析，包括对初始值和模型的三个参数的敏感性分析。我们表明，所考虑的模型非常适合某些实际数据集，这些数据集涉及COVID-19爆发期间受感染个体数量的增长以及软件故障数据。拟合优度是根据ISRP指标和\（d_2 \）建立的-距离。我们还分析了两个时间非均匀的随机过程，即出生-死亡过程和出生过程，其均值与建议的增长曲线相等。在第一种情况下，我们获得了最终灭绝的可能性，吸收终点为0。我们还针对拟议的增长曲线和相应的出生过程处理阈值交叉问题。后一过程的仿真过程也被采用。