A new simultaneous disturbance estimation and fault reconstruction design is studied for stochastic distribution system with actuator faults and output disturbances, where the available information is the measured output probability density function (PDF) of the considered system. Based on this framework, the square-root rational B-spline neural network is applied to model the nonlinear dynamic between PDF and input, where the nonlinearity is assumed to meet the Lipschitz conditions with non-predetermined Lipschitz constants. In addition, a robust descriptor observer is designed to estimate the states and disturbances simultaneously. Meanwhile, the maximum admissible Lipschitz constant is derived via convex optimization. Then, a sliding mode scheme is proposed for the designed observer to reconstruct the actuator faults. Finally, a soil particle gradation control (SPGC) is carried out to show the effectiveness of this way.