There are numerous uses of Global Navigation Satellite Systems (GNSS): navigation, of course, but also various optimizations, such as routing or handover protocols in telecommunication networks. Moreover, energy saving approaches may also be based on the use of the locations of the various entities involved. Most of the time, the positioning is considered to be "perfect": no uncertainty on the values, sometimes leading to inappropriate results and conclusions concerning the above-mentioned optimizations. This paper intends to provide the various communities with a simple, proved and easy to use statistical model of the error distributions of the GPS positioning. A large measurement campaign has been carried out in order to provide the model with a representative base of GPS data. The receiver used is a ublox 6T for raw data and it has been associated with the free RTKLIB software for data processing. We have highlighted that a specific parameter, called "Cost" and defined in the paper, can be used in order to completely define the model. Since this parameter can be estimated from the receiver, the model can thus either be used in real time or in post processing, or even included in any optimization scheme. The proposed model has been validated in various environmental conditions that have a great impact on the distributions of the positioning error and on the accuracy of GPS receivers