Growth Models With Oblique Asymptote

Abstract

A class of smooth functions which can be used as regression models for modelling phenomena requiring an oblique asymptote is analyzed. These types of models were defined as a product of a linear function and some well known growth models. In addition to their increasing character with an oblique asymptote, the resulting models provide curves with a single inflection point.

Least squares fitting of the stage–discharge relationship using smooth models with curvilinear asymptotes

“…The case 0 < β < 1 gives an increasing concave asymptote with an odd or even number of inflection points, the parity of the number of inflection points depends on the values of the parameters p and β of the function m t ð Þ. The limiting case β ¼ 1 generates an oblique asymptote with one inflection point (Dubeau and Mir 2013). The case p = 0 retrieves the natural horizontal asymptote of the basic model f t ð Þ.…”