Modeling and analysis of biological growth curves are an age-old study area in which much effort has been dedicated to developing new growth equations. Recent efforts focus on identifying the correct model from a large number of equations. The relative growth rate (RGR), developed by Fisher (1921), has largely been used in the statistical inference of biological growth curve models. It is convenient to express growth equations using RGR, where RGR can be expressed as functions of size or time. Even though RGR is model invariant, it has limitations when it comes to identifying actual growth patterns. By proposing interval-specific rate parameters (ISRPs), Pal et al. (2018) appeared to solve this problem. The ISRP is based on the mathematical structure of the growth equations. Therefore, it is not model invariant. The current effort is to develop a measure of growth that is model invariant like RGR and shares the advantages of ISRP. We propose a new measure of growth, which we call instantaneous maturity rate (IMR). IMR is model invariant, which allows it to distinguish growth patterns more clearly than RGR. IMR is also scale-invariant and can take several forms including increasing, decreasing, constant, sigmoidal, bell-shaped, and bathtub. A wide range of possible IMR shapes makes it possible to identify different growth curves. The estimation procedure of IMR under a stochastic setup has been developed. Statistical properties of empirical IMR estimators have also been investigated in detail. In addition to extensive simulation studies, real data sets have been analyzed to prove the utility of IMR.

生物生长曲线的建模和分析是一个古老的研究领域，人们致力于开发新的生长方程。最近的工作重点是从大量方程中识别正确的模型。相对生长率（RGR）由Fisher（1921）提出，主要用于生物生长曲线模型的统计推断。使用 RGR 可以方便地表达生长方程，其中 RGR 可以表示为大小或时间的函数。尽管 RGR 是模型不变的，但它在识别实际生长模式时存在局限性。Pal 等人提出了特定区间速率参数 (ISRP)。（2018）的出现解决了这个问题。ISRP 基于增长方程的数学结构。因此，它不是模型不变的。当前的工作是开发一种像 RGR 一样具有模型不变性的增长度量，并具有 ISRP 的优点。我们提出了一种新的增长衡量标准，称为瞬时成熟率（IMR）。IMR 是模型不变的，这使其能够比 RGR 更清楚地区分生长模式。IMR 也是尺度不变的，可以采用多种形式，包括递增、递减、常数、S 形、钟形和浴盆形。多种可能的 IMR 形状使得识别不同的生长曲线成为可能。随机设置下的 IMR 估计程序已经开发出来。经验 IMR 估计量的统计特性也得到了详细研究。除了广泛的模拟研究之外，还对真实数据集进行了分析，以证明 IMR 的实用性。