Normal distributions are ubiquitous, but many actual distributions are different from normal—for example, they are skewed. To describe such distributions, it is desirable to have a few-parametric family that extends the family of normal distributions. Several such families have been proposed. Empirically, the most effective among them is the family of so-called skew-normal distributions first proposed by A. Azzalini. In particular, this family is effective in econometrics. In this paper, we provide a theoretical explanation for this empirical success. This explanation is similar to an explanation of what ReLU activations functions are most effective in deep learning.