Inspired by the thermodynamic averaging, we introduce other statistical transformations of the Boltzmann weighted energy distribution, like its standard deviation. To describe the multi-modality of the energy distribution, we also introduce the Boltzmann weighted skewness and kurtosis; we can then deduce the Sarle's bimodality coefficient of Boltzmann weighted interaction energies. We can also retrieve statistical measures from the grid values of interaction energy as descriptors, without weighing by Boltzmann factors, to give a richer description of the distribution. For instance, the model uses the mean and standard deviation of this distribution calculated for xenon and krypton.