The maximum entropy criterion for estimating an unknown probability density function from its moments is applied to the evaluation of the average error probability in digital communications. Accurate averages are obtained, even when a few moments are available. The method is stable and results compare well with those from the powerful and widely used Gauss quadrature rules (GQR) method. For test cases presented in this work, the maximum entropy method achieved results with typically a few moments, while the GQR method required many more moments to obtain the same, as accurately. The method requires about the same number of moments as techniques based on orthogonal expansions. In addition, it provides an estimate of the probability density function of the target variable in a digital communication application.