We investigate the modeling of commodity prices that exhibit "fat tails" in the empirical marginal distributions. Using electricity price data, we explore the goodness-of-fit of different classes of distributions with an emphasis on capturing the fat tails in the data. Specifically, we fit empirical marginal distributions of time series data to distributions with either quantile functions or probability density functions in closed-forms. The theoretical distributions under consideration all have rich tail behaviors that enable us to model the heavy tails in the commodity prices caused by jumps and stochastic volatility. The fact that the theoretical distributions are easy to simulate makes the models appealing since the tasks of parameter estimation and derivative pricing can be directly implemented based on observed market data.