The time scale of usual hydrological applications can vary from a few minutes to a few days. An accurate description of the precipitation probability distributions at the appropriate time scale is needed to compute meaningful summaries like return levels and periods. However few statistical parametric models can handle the full rainfall distribution at these different temporal scales. In this context, we propose and study a new meta-Gaussian model which leads to a parametric model with four parameters for the full distribution of precipitation. The main advantage of our model is that it can be applied to a wide range of accumulation periods. In particular, it still performs well below the hourly scale. In addition, each parameter is linked to a different part of the distribution: one of them describes the probability of rainfall occurrence, two parameters are related respectively to the shape of lower and upper tails of the distribution, and the last one is a multiplicative scale parameter. The building block of our model is the use of a latent Gaussian process that offers flexibility and simple inference algorithms. The model is fitted to rain gauge data recorded in Guipavas (France). It is shown that the proposed distribution handles accumulation periods from 6 minutes to several days. The model outperforms other meta-Gaussian models which have been proposed in the literature.