Accurate watch time prediction is crucial for enhancing user engagement in streaming short-video platforms, although it is challenged by complex distribution characteristics across multi-granularity levels. Through systematic analysis of real-world industrial data, we uncover two critical challenges in watch time prediction from a distribution aspect: (1) coarse-grained skewness induced by a significant concentration of quick-skips1, (2) fine-grained diversity arising from various user-video interaction patterns. Consequently, we assume that the watch time follows the Exponential-Gaussian Mixture (EGM) distribution, where the exponential and Gaussian components respectively characterize the skewness and diversity. Accordingly, an Exponential-Gaussian Mixture Network (EGMN) is proposed for the parameterization of EGM distribution, which consists of two key modules: a hidden representation encoder and a mixture parameter generator. We conducted extensive offline experiments on public datasets and online A/B tests on the industrial short-video feeding scenario of Xiaohongshu App to validate the superiority of EGMN compared with existing state-of-the-art methods. Remarkably, comprehensive experimental results have proven that EGMN exhibits excellent distribution fitting ability across coarse-to-fine-grained levels.