The present research concerns the dynamical mistuning analysis of a rotating bladed-disk for which nonlinear geometrical effects can occur, in which the mistuning phenomenon is taken into account using a probabilistic approach of uncertainties. An alternative strategy to [1], where the mistuning is described by using a nonparametric probabilistic approach based on random matrix theory for modeling the random operators of a reduced-order computational model, is proposed. It is based on the use of a new nonparametric probabilistic approach of model-form uncertainties [2]. The deterministic vector basis, which is obtained from the Proper Orthogonalization Decomposition method, is replaced by a stochastic reduced-order basis (SROB). Each realization of the SROB respects some mathematical properties linked to the available information under constraints concerning the specified boundary conditions and the usual orthogonality properties. With such strategy, it is necessary to compute the stochastic nonlinear reduced internal forces combining the use of the SROB with the finite element method. There are hyper-parameters that control the uncertainties in the structure and its calibration with respect to experimental data is investigated. The numerical application is a rotating mistuned bladed-disk subjected to a load for which geometrical nonlinearities effects occur. [1] E. Capiez-Lernout, C. Soize, and M. Mbaye. Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity. Journal of Sound and Vibration, 356(11):124?143, 2015. [2] C. Soize and C. Farhat. A nonparametric probabilistic approach for quantifying uncertainties in low dimensional and high-dimensional nonlinear models. International Journal for Numerical Methods in Engineering, 109(6):837-888, 2017.