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In this work, a novel robust fault detection algorithm is investigated for stochastic distribution systems with multiple uncertainties, where the output is characterised by its measured output probability density function. By constructing an auxiliary augmented stochastic descriptor system, the original stochastic distribution system is transferred into a descriptor system subjected to model uncertainties, where a proportional and derivative descriptor estimator is developed to solve the fault detection problem. The system input and the output probability density function are used in the design of this estimator. Furthermore, the derivative gain of the estimator is chosen to attenuate the output uncertainties, and the free parameters embedded inside the proportional gain are selected to generate an optimally robust residual signal for fault detection so as to achieve a situation where this residual signal is sensitive to system faults while insensitive to model uncertainties, input disturbances and output noises. A numerical example is given, and the simulation result shows satisfactory detection performance.