Is there something like a Root Mean Square Relative Error (RMSRE)? Or: What is the name of this error? \begin{equation}
\text{RMSRE} = \sqrt{\frac{1}{n}\cdot\sum_{i=1}^n \Delta X^2_{\text{rel},i}}
\end{equation}
with 
\begin{equation}
 \Delta X_{\text{rel},i} = \frac{X_i}{T_i}-1,
\end{equation}
where $T_i$ is the desired value and $X_i$ is the actual value.
If this error actually exists, then a citable source for it would be greatly appreciated. If it does not exist, then why so?
Thanks in advance.
 A: Short answer : It exists and here is the reference and also there is a similar post regarding difference between RRMSE & RMSRE I would like to draw your attention. It depends where you apply division to make error relative! 
Mathematically, when you divide the difference between the predicted output and actual(expected) output $T_i-X_i$  by $T_i$ then error will be considered Relatively
which means that each residual is scaled against actual value or normalized by that . 
\begin{equation}
 \Delta X_{\text{rel},i}=\frac{X_i-T_i}{T_i}
\end{equation}
\begin{equation}
\text{RMSRE} = \sqrt{\frac{1}{n}\cdot\sum_{i=1}^{n}\Delta X^2_{\text{rel},i}}
\end{equation}
\begin{equation}
\text{RRMSE} = \sqrt{\frac{\frac{1}{n}\cdot\sum_{i=1}^{n}(X_i-T_i)^2}{\sum_{i=1}^{n}T_i^2}}
\end{equation}
\begin{equation}
\text{PRMSE} = \sqrt{\frac{\frac{1}{n}\cdot\sum_{i=1}^{n}(X_i-T_i)^2}{\sum_{i=1}^{n}T_i^2}}\cdot 100 \%
\end{equation}
Another reference for using RRMSE could be found here and the last form is known as rRMSE as well  as shown here
Basically we same approach is used in MAPE to express error either relatively or in form of percentage as the last form. Obviously expression in form of percentage itself includes  relative error.  
