*4.2. Evaluation*

**Exponential distribution:** We performed a Kolmogorov–Smirnov (KS) goodness-of-fit test to validate the assumption that inter-arrival times of EV sessions follow the exponential distribution.

**Arrival models:** Once the *AM* was trained using the 2015 EV session data, a synthetic sample for 2015 could be generated. This sample was to generate EV arrivals from January 1, 2015 to December 31, 2015. We generate 10 samples for each modeling method (three IAT models and two AC models). EV arrivals were aggregated on an hourly and daily basis. Since the aggregated values represent count data, we used a non-parametric Wilcoxon test to assess similarity between the generated samples and the actual data. We performed the test on a monthly basis for the daily aggregated data and on an hourly basis for hourly aggregated data. We provide plots for visual comparison.

**Mixture models:** Connection times were sampled from the fitted GMMs, for the actual EV arrivals. Density plots were created to evaluate whether the peaks of the conditional probability distributions were modeled correctly. A similar evaluation was preformed for required energy.

**SDG:** Final generated data (and actual data) were 3-dimensional, with each session defined by (*ta*, *tc*, *E*). The actual data comprised 350,000 sessions, and the numbers of sessions in the generated samples were of the same order. Since two-sample similarity tests for high dimensional data become unreliable as the data size increases, we used a kernel density estimation (KDE) test [21] and a multidimensional version of the KS test [22,23]. We did those tests for (*ta*, *tc*) and (*ta*, *E*) combinations.

In this section we defined different methods for fitting the parameters of SDG. Depending on the modeling method, the parameters of SDG will also change ( *λ* in case of the exponential distribution, and (*μ* , *α*) in case of the negative binomial distribution).
