In transient nonlinear structural dynamics, the dynamical levels of transient vibrations can be defined in terms of a shock response spectrum (SRS) in order to specify the transient loads which are applied to an equipment or to a secondary subsystem. A fundamental problem is then to construct a generator of the non-stationary stochastic process (the transient signal) satisfying a given SRS. This problem has been looked at by many scientists in using specific representations of the non-stationary stochastic process (the accelerogram). In this paper, we propose to solve this challenging stochastic inverse problem by another way in using Information Theory. In the approach proposed, the target SRS is taken as the mean value of the unknown random SRS spanned by the unknown non-stationary stochastic accelerogram for which the probabilistic model has to be constructed. We present the construction of the probability model which allows the confidence region of the random SRS to be carried out. The method presented is validated with an example.