Quantile Estimation Using the Log-Skew-Normal Linear Regression Model with Application to Children’s Weight Data

Abstract

In this article, we establish properties that relate quantiles of the log-skew-normal distribution to its parameters, allowing us to investigate the relationship between quantiles of a positive skewed response variable and a set of explanatory variables via the log-skew-normal linear regression model. We compute the maximum likelihood estimates of the parameters through a correspondence between the log-skew-normal and skew-normal linear regression models. Monte Carlo simulations show the satisfactory performance of the quantile estimators. An application to children’s data is presented and discussed.

Keywords

• child growth standards
• non-normal regression models
• quantile modeling
• skew-normal distribution