Distributed multiple-input multiple-output (MIMO) radars can use multiple transmitters and receivers simultaneously to detect targets.In order to maximize the probability of target detection,it is necessary to allocate the available transmit power resources suitably. The optimal allocation requires calculating the probability of detection, which is a computationally complex task, so using the exact distribution is very difficult in a dynamic scenario.In order to alleviate this problem,we propose an approximate distribution that is computationally simpler. This approximation is compared with the exact distribution as well as other cost functions that depend on the distribution of the test statistic, including the Kullback-Leibler divergence. It is demonstrated that the approximate distribution works well in the power allocation problem for MIMO radar target detection.