A Natural Goodness­of­Fit Test for the Exponential Growth Curve Model Based on the Relative Growth Rate

Abstract

This paper develops a natural goodness-of-fit test for the exponential growth curve model (EGCM) based on the property of finite differences. The EGCM has wide applications in various scientific fields such as biology, ecology, demography, population dynamics, finance, econometrics etc. Hill (1968, Biometrics, 4, 192-196) proposed a test for the polynomial growth curve model (PGCM) based on finite differences of the size variable. However, the PGCM has limited practical use and does not have any biologically interpretable para.ffieters. In comparison, the exponential model is more realistic and biologically meaningful; a goodness-of-fit test for the EGCM has substantial practical value. Bhattacharya et. al. (2004) generalized Hill's approach to the case of the EGCM based on appropriate finite differences of functions of the size variable. In this paper we present an alternative test for the EGCM by directly modeling the relative growth rate (rather than the size variable itself) and hence avoid the assumptions necessary in Bhattacharya et al (2004). The performance of the theory developed is illustrated with several sets of real data and through simulation. AMS {2000} Subject Classification: 62F03, 62P10.