This paper compares the performances of five members of the Generalized Hyperbolic family of distributions (i.e., the Generalized Hyperbolic (GH), Hyperbolic (HYP), Normal Inverse Gaussian (NIG), Hyperbolic Skew Studentís t (SSt) and Variance-Gamma (VG) distributions) alongside the Gaussian as benchmark in fitting log returns of an Electricity Futures Contract. Using log likelihood (LLH) function and Akaike Information (AIC) as criteria for selection, the GH and NIG outperformed other models, having 49.8% and 49.6% weight of evidence in their favour respectively for being the two models that give the best prediction of the log returns. However, simulation results show that GH is the most consistent among the candidate distributions especially in large sample situations. The tails behaviour of these distributions show that the SSt overestimates while the HYP and VG underestimate the probability of rare events in the electricity market at both tails. Results show that these distributions have substantial heavy tails.