We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.

翻译：假设预测误差服从一个在非负实数上对称且单调非增的概率分布，若观测值与预测值之间存在偏差，则我们遭受损失。在该假设下，我们求解了一个带非对称损失函数的最小化问题。此外，我们给出了该损失方差的一个不等式。