## 1 Introduction  
In the last decades, probabilistic forecasting has drawn a lot of attention in the scientific community, which has led to the fast-paced development of new methods as well as applications in a wide variety of domains, including renewable energies [1, 2, 3], weather forecasting [4, 5, 6], seismic hazard prediction [7, 8], and health care [9]. Autoregressive conditional heteroscedasticity (ARCH) [10] and generalized autoregressive conditional heteroscedasticity (GARCH) [11] are two of the pioneer models for probabilistic forecasting. These methods try to model the variance in future value alongside forecasting the mean of future outcomes. Many other models have been proposed based on the ARCH method, and they have been utilized in various domains, especially in the finance domain [12, 13, 14]. Furthermore, researchers have proposed probabilistic forecasting models based on Gaussian processes [15, 16]. These models have higher resistance against overfitting and can capture highly nonlinear relationships without increasing model complexity. Recently, several approaches for probabilistic forecasting based on neural networks have been proposed. These models can efficiently incorporate a large amount of data and do not require manual feature engineering. Explicit models assume the type of uncertainty in data explicitly and learn the parameters of the assumed distribution accordingly. DeepAR [17] is one of the successful examples of the explicit modeling of the predictive future distribution of data. On the other hand, implicit models employ generative models for probabilistic forecasting. Implicit models do not make any assumption about data uncertainty and learn the data distribution from given samples, i.e., a dataset. Hence, they do not have direct access to the probability distribution of the model over future values and provide future values by forecasting through Monte-Carlo sampling. Some prominent neural-network-based implicit probabilistic forecast models are low-rank Gaussian copula processes [18], conditioned normalizing flows [19], normalizing kalman filters [20], the denoising diffusion model [21], models based on variational auto-encoders (VEAs) [22; 23; 24] and conditional generative adversarial networks (CGANs) [25; 26]. The assessment of these forecasting models poses a special challenge, and it is important to have evaluation methods that can be used to gauge their performance. [PERSON] et al. [27] coined the concept of scoring rules for summarizing the quality of a probabilistic forecaster with a numerical score [28]. A scoring rule is expected to make a careful assessment and be honest [27]. [PERSON] et al. [28] proposed the continuous ranked probability score (CRPS) for univariate and energy score (ES) for multivariate time series as strictly proper scoring rules. While CRPS presents a robust and reliable assessment method for univariate time-series forecasting, ES's discrimination ability diminishes in higher dimensionalities [29]. Several other multivariate metrics [29; 30] have been proposed to address probabilistic forecaster assessment in higher dimensions, however, each of them has a flaw that makes them unsuitable for the assessment task. For instance, variogram score [30] is a proper scoring rule which can reflect the misalignment in correlation very well, but it lacks the strictness property. The Dawid-Sebastian score [31] employs only the first two moments of distribution for evaluation, which is not sufficient for many applications. A thorough analysis of these metrics is provided in [32]. Recently, [PERSON] et al. [18] suggested CRPS-Sum as a new proper multivariate-scoring rule. This scoring rule has been well-received in the scientific community [18; 19; 20; 21]. The properties of CRPS-Sum have not been studied so far. In this paper, our goal is to discuss the discrimination ability of CRPS-Sum. We conducted several experiments on artificial and real datasets to investigate the quantification power of CRPS-Sum for the performance of a probabilistic forecaster.