Curve Fitting with Smooth Functions That are Piecewise-Linear in the Limit

Abstract

Many data are suitably modeled by functions consisting of straight-line segments. These functions may be called piecewise-linear. Smooth functions that are related to the hyperbola and that have piecewiselinear functions as limiting forms are particularly useful for response curves with known asymptotic behavior. Least-squares fitting of such functions to irrigated-corn-yield data from three sites shows that these functions are capable of adequately representing the data; Mitscherlich and linear-response-andplateau models are not flexible enough to adequately represent the data at aft three sites. An advantage of these functions is that they possess continuous derivatives of all orders and are therefore readily applicable to economic or other types of analysis where smooth functions are preferred. The general form of the functions is a summation that may have any desired number of terms and, therefore, may represent simple or highly complex situations, as needed.