Data weighting was demonstrated as an adequate approach to determine the DRT of a battery that shows typical heteroscedasticity of noise. Stochastic residuals without any non-random systematic features were obtained after a DRT fit, indicating that no information was lost during the DRT step. It was demonstrated that GPR can be used for model-free estimation of weights based on a single data set only. The obtained distributions were consistent with DRT obtained using a statistical noise analysis of multiple repetitions of the same experiment.