Recently, suction buckets have become a very prominent foundation for bottom fixed and floating offshore wind turbines. They are embedded with an installation force that stems from water evacuation inside the bucket. This internal negative pressure leads to a high risk of structural buckling. The buckling strength is significantly reduced by geometric imperfections. In previous work, equivalent geometric imperfection forms were introduced and the lower bound was evaluated. However, it has not yet been possible to identify a generally appropriate imperfection form. A probabilistic design approach based on realistic imperfections was not yet considered for suction buckets. Therefore, in this work, a stochastic modeling approach is introduced, which bases on measured data. The imperfection is decomposed to the half-wave cosine Fourier representation. Realizations of the imperfection pattern are generated by filtering white noise with the amplitude spectrum. They are then applied as out of plane deviations on a geometrically and materially nonlinear finite element model and evaluated. The resulting buckling pressure distribution can then be evaluated for different reliability levels. By considering more realistic imperfections and a plastic soil model, the buckling pressure increases by up to a factor of two compared to the conservative stress-based buckling approach.