Preprint Technical Note Version 1 Preserved in Portico This version is not peer-reviewed

# A Note on Novel Normal-Power Non-Linear Function

Version 1 : Received: 8 March 2022 / Approved: 11 March 2022 / Online: 11 March 2022 (10:07:40 CET)

How to cite: Ekum, M.I. A Note on Novel Normal-Power Non-Linear Function. Preprints 2022, 2022030166. https://doi.org/10.20944/preprints202203.0166.v1 Ekum, M.I. A Note on Novel Normal-Power Non-Linear Function. Preprints 2022, 2022030166. https://doi.org/10.20944/preprints202203.0166.v1

## Abstract

Regression models are mostly used in all fields of sciences for modelling the relationship between a dependent variable and independent variable(s). The least square method is often used to estimate the parameters in a linear model because it is the best linear unbiased estimator. These estimates can only be reliable if the assumption of normality is satisfied. In some cases the dependent variable might be bimodal and shows a non-linear relationship with the independent variable(s). In this case, a non-linear model should be used. In non-linear model, the standard errors are often obtained by linearizing the nonlinear function around the parameter, assuming central limit theorem. After the linearization, the least square parameter estimates are obtained. It should be noted that the error of the non-linear model is different from that of the transformed linear model. Thus, there is a need to transform back to the original non-linear model. In this note, a novel non-linear function was developed into a non-linear regression model, called Normal-Power model. The least square method was used to estimate the parameter of the transformed model. Its usefulness in regression model was demonstrated using real data of Nigeria Economy-Tourism model.

## Keywords

Bimodal Dependent Variable; Normal-Power; Non-Linear; Least Square Estimation; Economy-Tourism Model

## Subject

Computer Science and Mathematics, Probability and Statistics