Since its inception, stochastic Data Envelopment Analysis (DEA) has found many applications. The approach commonly taken in stochastic DEA is via chance constraint models. This approach cannot, however, capture the inherent random fluctuations of the efficiency score caused by the random nature of the input and output variables. Having taken a random efficiency perspective, one can introduce an alternative approach that provides ground for capturing these fluctuations. One aspect of this alternative approach, which seems to have been neglected, concerns the distribution of the random efficiency score. We show that the efficiency score does not have a continuous distribution even if the random input and output variables distributions are continuous. The efficiency score distribution has, in fact, a point mass decomposition at 1. This observation renders the non-parametric bootstrap of efficiency score impossible. We introduce several criteria for the ranking and classification of Decision Making Units (DMUs) using a random efficiency perspective, including an interactive ranking method that incorporates managers' knowledge and preferences. We then apply the point mass decomposition of efficiency score distributions of DMUs and show how these criteria can be implemented. We also discuss how one may estimate the efficiency score distributions of DMUs using both Bayesian and frequentist approaches. Our proposed methodology is illustrated using a real data set.