A New Growth Rate Measure in Identifying Extended Gompertz Growth Curve and Development of Goodness-of-fit Test

Growth is a fundamental aspect of a living organism. Growth curves play an important role in explaining the complex dynamics of growth trajectories. The development of a large class of growth models provides more choices to explain complex growth dynamics. However, identifying a suitable growth curve from a broad class of growth models becomes a challenging task. Relative Growth Rate (RGR) is the most popular measure in the growth-related study. It serves many purposes in growth curve literature, including constructing any goodness-of-fit index of some growth dynamics. However, the goodness-of-fit test based on RGR is restricted to only simple growth models. This study aims to develop a new growth rate function, instantaneous maturity rate (IMR), which can play an important role in identifying growth models. We have explored that the measure has synergy in mathematical form with IMR. However, unlike the hazard rate, IMR is a random variable when the size/RGR variable is stochastic. We have derived the exact and asymptotic distribution of this measure under the Gaussian setup of both the size and RGR variables. We have constructed a goodness-of-fit test for the extended Gompertz growth model based on the instantaneous maturity rate. We have checked the performance of the test through simulation studies as well as real data. AMS 2010 subject classifications: 62Mxx, 92Bxx, 62P10