We have investigated three models currently used for the spectral power distributions of single color LEDs. We present empirical models using a single and a double Gaussian distribution, and a model using principles from solid state physics, further more we show how the model parameters are expected to vary with current and junction temperature. Commercial high power blue LEDs were measured with respect to spectral distribution and chromaticity and the result was compared with the model predictions. We have found that the models predict significantly different results with respect to chromaticity and other color characteristics. The model that fits measurements best has chromaticity within a 5-step MacAdam ellipsis, and the worst preforming model a 12-step MacAdam ellipsis away from the measured chromaticity. We also show a method to infer internal characteristics of the the LED using the spectral power distribution such as the quasi Fermi level, density of states parabolicity, and band gap.