Here, a power allocation method jointly optimising the total transmit power and the probability of interception is proposed based on target detection applications in distributed multiple-input multiple-output (MIMO) radars. Power allocation is performed by solving a non-linear constrained optimisation problem formulated to minimise the total transmit power based on target detection applications. Then, the Neyman-Pearson detector is designed under the Rayleigh scatter model and the Lagrangian method is used to solve the optimisation problem. Moreover, a positioning algorithm optimising the placement of transmitters and receivers in distributed MIMO radars is applied to minimise the total transmit power satisfying the target detection criterion. The results show that uniform power allocation is not the optimal strategy and the proposed power allocation algorithm provides either better target detection performance for the same power budget, or requires less power to provide the same detection performance. Numerical simulations and the theoretic analysis confirm the effectiveness of the proposed algorithm.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.