Prediction-error expansion (PEE) by employing asymmetric prediction-error distribution (PED) provides an opportunity to decrease the embedding distortion in reversible data hiding (RDH). Nevertheless, its performance is completely dependent on the asymmetry rate of utilized PED which has never been studied before despite its crucial role in the performance of RDH algorithms. In this paper, a new prediction scheme called dynamic asymmetric distribution of error (DADE) is proposed for PEE. DADE predictor produces error distribution with dynamic asymmetry rate proportionate to embedding capacity (EC). In the proposed predictor several PEDs with a variety of asymmetry rates are composed and for a given EC, the PED with the highest asymmetry rate is selected, provided that it fulfills the EC. By increasing the asymmetry rate of the PED, the length of its short tail and the number of prediction errors in that part are reduced. Consequently, data embedding through single side expansion of prediction-error in the shorter side significantly decreases the number of shifted pixels which leads to the reduction of embedding distortion. Experimental results prove that the proposed method reduces the embedding distortion while slightly increases the EC of PEE based methods with asymmetric PED, and outperforms some state-of-the-art methods.