A unitary framework for the analysis of noise induced phenomena in complex hysteretic systems is developed and implemented in an open-access academic software. Various differential, integral, and algebraic models of hysteresis are considered while the input processes are generated from arbitrary given spectra. The statistical algorithm based on Monte-Carlo techniques and used to compute the stochastic characteristics of hysteretic systems is presented, along with several tests against analytical results available in the literature. This approach can be used to study various stochastic aspects of hysteresis, including thermal relaxation, data collapse, field cooling/zero field cooling, and noise passage. Several numerical simulations of noise induced phenomena in complex hysteretic systems are presented and their general qualitative features are discussed.