Abstract
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.
Highlights
Constructing growth curves describing dynamic evolutions is relevant to several applied fields
In order to propose a flexible growth model representing a generalization of various previous instances, we assume that X has a generalized Pareto distribution (GPD) with survival function
In many cases modelers are forced to perform the analysis on the ground of several curves aiming to compare the pertaining results and to detect the best choice on the basis of suitable statistical indexes
Summary
Constructing growth curves describing dynamic evolutions is relevant to several applied fields. Along the lines of the above mentioned researches, the present paper is aimed to propose a suitable extension of the celebrated Gompertz model This is a well-known growth model that is frequently adopted among the sigmoid models for fitting real data, and is governed by the following differential equation: d. The analysis is developed towards the more interesting case of a time-inhomogeneous linear birth process In both cases we specify the conditions that allow the mean of the process to be identical to the proposed generalized Gompertz growth curve. The second application is devoted to software failure data from Tandem Computers In this case, it is shown that the proposed model provides the better fit of the considered data under the ISRP metric and the d2-distance.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
