The skew-normal (SN) distribution is widely used for modeling skewed data due to its analytical tractability and flexibility. However, its unimodal nature limits its ability to describe more complex structures such as multimodality. In this work, we introduce a new generalization of the SN family, termed the tau skew-Normal ( \(\tau \) SN) distribution. The model incorporates an additional shape parameter \(\tau \) that controls both the number and intensity of modes, while preserving the interpretability and simplicity of the SN formulation. We demonstrate that the proposed distribution is identifiable and admits a simple stochastic representation, which facilitates simulation and inference. In the univariate case, we derive closed-form expressions for the moments and discuss its relationship with the SN distribution. In the multivariate extension, we show that univariate marginals remain within the same family. Parameter estimation is carried out via maximum likelihood, with performance assessed through Monte Carlo experiments. Finally, we include an application to bivariate financial data with heterogeneous behavior.
