Bridging calculus and statistics: Null - Hypotheses underlain by functional equations

Abstract

Statistical interpretation of Cauchy functional equation f(x+y)=f(x)+f(y) and related functional equations is suggested as a tool for generating hypotheses regarding the rate of growth: Linear, polynomial, or exponential, respectively. Suggested approach is based on analysis of internal dynamics of the phenomenon, rather than on finding best-fitting regression curve. As a teaching tool, it presents an example of investigation of abstract objects based on their properties and demonstrates opportunities for exploration of the real world based on combining mathematical theory with statistical techniques. Testing Malthusian theory of population growth is considered as an example. © Springer Science+Business Media B.V. 2010.