Precipitation amounts at daily or hourly scales are skewed to the right and heavy rainfall is poorly modeled by a simple gamma distribution. An important, yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire-range of rainfall amount. This model is based on a recent parametric statistical model called the class of Extended Generalized Pareto Distributions (EGPD). The EGPD family is in compliance with Extreme Value Theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a non-parametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical Generalized Pareto Distribution (GPD), the later being only fitted to excesses above high threshold. We also apply our semiparametric version of EGPD to daily rainfall data recorded at Mont-Aigoual weather station in France.