Based on statistical analyses of transform coefficients, we suggest estimations of bit-rate and distortion functions directly from spatial-domain statistics. Simulations show that the proposed rate and distortion estimators achieve similar results as the true Rate-Quantization (R-Q) and Distortion-Quantization (D-Q) curves. By exploiting the proposed statistical estimations, two major applications are suggested. One is the fast Rate-Distortion Optimized (RDO) mode decision and the other is the improved Rate Control (RC) in video encoding. Simulation results show that the rate-distortion estimators have sufficient accuracy such that we could achieve considerably better performance in both applications. We achieved 51.69% R-D cost computation time reduction in average for the rate-distortion optimized mode decision, and a 0.20 dB average Peak Signal-to-Noise Ratio (PSNR) improvement for rate-control in H.264/AVC, respectively.