Skewed and Flexible Skewed Distributions: A Modern Look at the Distribution of BMI

TLDR: In this paper, the authors used maximum likelihood estimation method to find distributions that best model body mass index (BMI) data and compared them to more conventional distributions, such as skew-normal and skew-t distributions, using AIC and BIC and Kolmogorov-Smirnov (K-S) goodness-of-fit test.

Abstract: ABSTRACT The purpose of this study is to find distributions that best model body mass index (BMI) data. BMI has become a standard health indicator and numerous studies have been done to examine the distribution of BMI. Due to the skew and bimodal nature, we focus on modeling BMI with flexible skewed distributions. The distributions are fitted to University of Wisconsin–Eau Claire (UWEC) BMI data and to data obtained from National Health and Nutrition Survey (NHANES). The model parameters are obtained using maximum likelihood estimation method. We compare flexible models to more conventional distributions, such as skew-normal and skew-t distributions, using AIC and BIC and Kolmogorov-Smirnov (K-S) goodness-of-fit test. Our results indicate that the skew-t and Alpha-Skew-Laplace distributions are reasonably competitive when describing unimodal BMI data whereas Alpha-Skew-Laplace, finite mixture of scale mixture of skew-normal and skew-t distributions are better alternatives to both unimodal and bimodal conventional distributions. The results we obtained are useful because we believe the models discussed in our study will offer a framework for testing features such as bimodality, asymmetry, and robustness of the BMI data, thus providing a more detailed and accurate understanding of the distribution of BMI.