In recent years, many component-based real-time systems have been proposed as a solution to modular and easily maintainable distributed real-time systems. This paper proposes a methodology for estimating probability distributions of execution times in the context of such systems, where no access to component internal code is assumed. In order to evaluate the proposed methodology, experiments were conducted with components, and related compositions, implemented over CIAO and ARCOS. CIAO is a known real-time component-based middleware and ARCOS is a software framework devoted to the construction of real-time control and supervision applications, also developed over CIAO. The collected experimental data show that the proposed approach is indeed a good approximation for component execution time probability distributions.