Comparison between Biexponential and Robust Biexponential Nonlinear Models, Using Simulation

Samira Muhammad Salih; Hozan Taha Abdalla

doi:10.25098/1.3.32

Authors

Samira Muhammad Salih Statistics & Informatics Department, Administration & Economics College, University of Sulaimani, Sulaymaniyah, Iraq.
Hozan Taha Abdalla Statistics & Informatics Department, Administration & Economics College, University of Sulaimani, Sulaymaniyah, Iraq.

DOI:

https://doi.org/10.25098/1.3.32

Keywords:

Linear Regression, Nonlinear Regression, Robust Regression, Biexponential, Weight Functions, ANOVA, AIC, BIC

Abstract

The Science of statistics has become paramount importance in this age as a means and a tool for scientific method in research in all the various fields of science. Linear regression is a powerful method for analyzing data described by models which are linear in the parameters.

In this paper, we compared between nonlinear regression method and robust method. Nonlinear models tend to be used either when they are suggested by theoretical considerations or to build known nonlinear behavior into a model. Even when a linear approximation works well, a nonlinear model may still be used to retain a clear interpretation of the parameters. By using R language software we generate the data that we use in this paper for three sample sizes (25,50,100) and we took (200) reputations for each sample sizes. In the practical part of this thesis for Nonlinear Regression, we used Biexponential Nonlinear Regression Model and we estimate four parameters. We found the estimated parameters mean for our model, and we also found that the best performance for parameters by depending on the Akaike information criterion and Bayesian information criterion.We tested the parameters, so we found that they are significant also the ANOVA table where the F-test is significant.

The best model is Biexponential Robust Nonlinear Regression Model by depending on the parameters mean as an initial value from Biexponential Nonlinear Regression Model for sample size (100) because it has the minimum AIC and BIC.

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