Reliable and economical scheduling and operation of power systems requires an adequate representation of the electrical load's uncertainty. In contrast to point forecasting, which only capture the variability of demand, probabilistic forecasting can provide insights about its uncertainty to better support decision-making processes. This paper presents a case study showing the use of Mixture Density Networks (MDN) for probabilistic forecasting and scenario generation of hourly electrical load in four Chilean substations. An MDN is a class of neural network that outputs parameters of a mixture model, i.e., the parameters of a linear combination of probability distributions. While, in principle, MDN models with Normal distributions can serve as a reasonable approximate of the uncertainty, a large number of Normal components are necessary for adjusting asymmetrical or leptokurtic distributions. Thus, we complement the traditionally used Normal distributions with the use of the four-parameter Sinh-Arcsinh (SHASH) distribution family, as a single SHASH MDN component can adopt multiple third and fourth standardized moment values. We show that this approach reduces the forecasting error for four Chilean substation load series with different profiles.