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Internet-distributed hardware-in-the-loop simulation (ID-HILS) is emerging as a critical enabler for geographically dispersed concurrent systems engineering. This paper is concerned with transparency in ID-HILS, which is a measure of fidelity with respect to the nondistributed alternative of integration. Specifically, recognizing the need for a transparency analysis method for stochastic and nonlinear ID-HILS systems in general, the paper first proposes a statistical transparency analysis method. Next, this method is applied to a novel ID-HILS system. This application helps draw two important general conclusions: 1) Distributing the simulation can in and of itself be an important source of transparency degradation and can even dominate the adverse effects of the Internet's delay, jitter, and loss when delay is relatively small; and 2) transparency is not an independent property of the system, but is a system property that needs to be defined with respect to an output, as different output signals in the same system can experience different levels of transparency. These conclusions are important for guiding future efforts to improve transparency in a given ID-HILS system, and the proposed method enables such transparency analysis in other stochastic nonlinear ID-HILS systems, as well.