calculateRelativeRMSE.m File Reference

Function to calculate Relative RMSE. More...

Functions
function	calculateRelativeRMSE (in x, in y)
	Function to calculate Relative RMSE.

Detailed Description

Function to calculate Relative RMSE.

Author

Marlies Nitschke

Date

December, 2018

Function Documentation

calculateRelativeRMSE()

function calculateRelativeRMSE	(	in	x,
		in	y
	)

Function to calculate Relative RMSE.

This function will calculate the relative Root-Mean-Squared Error (RRMSE) or normalized RMSE. It indicates the relative fit of the model, that is, how close the observed data points are to the model's predicted values. It is normalized with respect to the average peak-to- peak amplitude. If the input is not a vector but a scalar, the average is used for normalization. As with the RMSE, lower relative RMSE values indicate better fit.

\( \mathbf{x} = \left[x_1,x_2,\ldots,x_N \right]^T \)

\( \mathbf{y} = \left[y_1,y_2,\ldots,y_N \right]^T \)

RMSE = \( \sqrt {\frac{1}{N} \displaystyle\sum_{i=1}^{N}\displaystyle (y_i - x_i )^2 } \)

Relative RMSE = \( \displaystyle\frac{RMSE}{\displaystyle\frac{1}{2} \sum_{i=1}^{2}[\max_{0<t<T}(u_i(t)) - \min_{0<t<T}(u_i(t)] } * 100\% \), if x and y are vectors

Relative RMSE = \( \displaystyle\frac{RMSE}{\displaystyle\frac{1}{2} \sum_{i=1}^{2}u_i(t) } * 100\% \), if x and y are scalars

[RMSE] = calculateRelativeRMSE(x, y)

Parameters

x	Double Vector x
y	Double Vector y

Return values

RMSE	Double: relative RMSE, between -100% and 100%)