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Probability density functions are estimated by an exponential family of densities based on multilayer feedforward networks. The role of the multilayer feedforward networks, in the proposed estimator, is to approximate the logarithm of the probability density functions. The method of maximum likelihood is used, as the main contribution, to derive an unsupervised backpropagation learning law to estimate the probability density functions. Computer simulation results demonstrating the use of the derived learning law are presented.< >