We have modeled electrostatic Langmuir waves by an electric field, consisting of superposition of Gaussian wave packets with several probability distributions of amplitudes and with several Poisson distributions of wave packets. The outcome of the model is that the WIND satellite observations, especially in the low frequency domain (the WAVES experiment), do not allow to conclude whether the input wave amplitude distributions are closer to the log-normal than to the Pearson type I or uniform. The average number of wave packets in 1 s is found to be between 0.1 and 50. Therefore, there is a clear need to measure Langmuir wave energy distributions directly at the waveform level, not a posteriori in the spectral domain. This is planned to be implemented on the RPW (Radio and Plasma Wave Analyzer) instrument in the Solar Orbiter mission.