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In this paper, we introduce a nonlinear model which can be used as a regression model for modeling phenomena requiring a two-phase growth curves. The proposed model is defined as a continuo...

In this paper we consider the problem of modelling the stage–discharge relationship by curve fitting using the least squares method. Our basic idea is to present new models which are more flexible and have the ability to model phenomena with increasing or unchanging carrying capacity. The new models present a generalization of some sigmoid smooth models commonly used in practice. They are characterized by a curvilinear asymptote and may have several inflection points. The use of these models on six real datasets collected from the US Geological Survey’s website proves their performance and their ability to model hydrological phenomena. Editor D. Koutsoyiannis; Associate editor S. Yue

We present a smooth function that can be used as regression curve for modeling growth phenomena requiring an increasing curvilinear concave asymptote. This model is obtained as the product of a concave asymptotic curve and the exponential model. In addition to its increasing character with a curvilinear asymptote, including horizontal or linear increasing asymptote, the resulting model provides curves with a single inflection point. Numerical examples are presented.

Given a set of data , we present sufficient conditions which guarantee the existence of the weighted least squares estimate for a three-parametric exponential function. To this end, we suggest a classification of the data based on their increasing or decreasing trend, and on their convexity or concavity form. We discuss a choice of the initial approximation and present a numerical example.

The best discrete least squares polynomial fit to a data set is revisited. We point out some properties related to the best polynomial and precise the dimension of vector spaces encountered to solve the problem. Finally, we suggest a basic classification of data sets based on their increasing or decreasing trend, and on their convexity or concavity form.

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.

The problem of using a non-linear function with only one inflection point for modelling hydrological phenomena is addressed. We present the examples of such functions and retain values of their parameters giving increasing function with one inflection point. For a set of data from one river, their least squares adjustments are compared for the stage-discharge relationship, namely the flow and the height of the water of a river. Finally we raise the problem of classifying rivers in terms of their best non-linear fitting model.