The Kumaraswamy normal linear regression model with applications

• Published in: Communications in statistics. Simulation and computation Vol. 47; no. 10; pp. 3062 - 3082
• Main Authors: Cordeiro, Gauss M., Machado, Elizabete C., Botter, Denise A., Sandoval, Mônica C.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 26-11-2018; Taylor & Francis Ltd
• Subjects: Diagnostic systems; Generating function; Kumaraswamy-normal distribution; Lehmann classes; Maximum likelihood estimates; Mean deviation; Moment; Normal distribution; Parameter estimation; Quantile function; Regression analysis; Regression models; Statistical analysis
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2017.1367808

For any continuous baseline G distribution, Cordeiro and Castro pioneered the Kumaraswamy-G family of distributions with two extra positive parameters, which generalizes both Lehmann types I and II classes. We study some mathematical properties of the Kumaraswamy-normal (KwN) distribution including ordinary and incomplete moments, mean deviations, quantile and generating functions, probability weighted moments, and two entropy measures. We propose a new linear regression model based on the KwN distribution, which extends the normal linear regression model. We obtain the maximum likelihood estimates of the model parameters and provide some diagnostic measures such as global influence, local influence, and residuals. We illustrate the potentiality of the introduced models by means of two applications to real datasets.