In this paper, we consider power allocation over multiple transmit antennas in a distributed transmit antenna system with delay diversity assuming that the power delay profile (PDP) is available for each transmit antenna. This paper demonstrates that the optimal power allocation for outage minimization greatly depends on the system's operating signal-to-noise ratio (SNR) range. With a low operating SNR, it is required to assign all power to the antenna closest to the receiver. On the other hand, when the operating SNR is sufficiently high, power must be allocated proportional to the number of the non-zero elements in the PDP for each antenna.