The generalized Gaussian class of noise densities is considered relative to detection probabilities for a recently proposed locally optimum discrete-time stochastic signal detector [H. V. Poor and J. B. Thomas, J. Acoust. Soc. Am. 63, 75–80 (1978)]. It is shown that for a noise density with a slower rate of decay in the tails than the Gaussian distribution that a non-Gaussian noise environment results in higher detection probabilities.