Entropy-Based Weighted Exponential Regression

The exponential regression model is one of the most important and famous non-linear regression models. It is widely used in many experimental applications. This paper used the concept of weighted distributions to propose a modified exponential distribution and derive new regression model. Accordingly, two new weight probability density functions based on Renyi entropy were proposed: the Entropy-Based Weighted Exponential Distribution (EB-WE) and Renyi Entropy-Based Weighted Exponential Distribution (REB-WED). In this context, we derived the statistical characteristics for REB-WED, including the moment measures such as the population mean and r-th moment. Also, the measures of variation including the variance, standard deviation and coefficient of variation are proposed. Moreover, the measures of shape (i.e., skewness, kurtosis) and reliability measures included the hazard function, the odd function and reliability function also discussed. The unknown parameters of all proposed distributions were estimated by using the maximum likelihood estimation method. Also, the regression models are derived and its performances are discussed thru a Monte Carlo simulation experiments using the mean squared error and the bias criterions. The simulation results and the real data analyses indicated that the REB-WE regression model is more accurate and more efficient than the EB-WE regression model.