New Class of Unit-Power-Skew-Normal Distribution and Its Associated Regression Model for Bounded Responses

Abstract

Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the (0,1) unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in (0,1); being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution.

Keywords

• unit distribution
• linear regression
• maximum likelihood estimation
• score function
• information matrix