In wireless sensor networks, multilevel quantization is necessary in order to find a compromise between small power consumption of sensors and good detection performance at the fusion center (FC) and generally, distance measures like J-divergence (JD) are used for quantization. This thesis proposes an approach based on maximizing the average output entropy of the sensors under both hypotheses named as maximum average entropy (MAE) method which is used in a Neyman-Pearson criterion based distributed detection scheme in order to detect a point source. Firstly, a deterministic signal with isotropic propagation model was considered. The receiver operating characteristics with multilevel MAE quantization of sensor outputs was evaluated both when the sensor outputs are available error-free at the FC and when they are transmitted using non-coherent communication via Rayleigh fading channels. Also sequential probability ratio tests of Wald were performed. Then, the case of spatially correlated sensors with a Gaussian isotropic event source was investigated. The computational requirements in evaluating multidimensional cumulative densities necessitated a rectangular grid model of sensor deployment and block-diagonal approximations of covariance matrix related to the event signal at the sensors without losing generality. The simulation studies show the success of MAE in the deterministic signal model and at six-level quantization its performance approaches that of non-quantized data transmission. In the sequential tests, again MAE was more successful compared to MJD resulting in smaller average sample numbers. It was observed that spatial correlation degrades system performance and MJD performs better in hypothesis tests based on change in variance.