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A method for evaluating the average error probability in digital fiber optic transmission systems is described. It takes into account the statistical properties of the main impairments that affect the information signal, i.e., shot noise (dark current included), thermal noise, and intersymbol interference. Unlike other methods, the analysis of shot-noise statistics does not entail the second-moment characterization alone, but uses a number of moments sufficient to evaluate the error probability with a high degree of accuracy. For this purpose it is shown how the cumulants of shot noise and intersymbol interference of any order can be computed. The baseband pulse response and the statistical distribution of the avalanche-photodetector gain are assumed to be available. Moreover, techniques for exploiting the cumulants are given; knowledge of the cumulants allows one to compute the probability of error by means of Gaussian numerical integration rules. Finally, some results and comparisons are reported.