Normalized RMSE (NRMSE) divides rmse() by the sample standard deviation of
observations.
Details
$$\mathrm{NRMSE}= \frac{\sqrt{n^{-1}\sum_{i=1}^{n}(obs_i-pred_i)^2}} {\sqrt{(n-1)^{-1}\sum_{i=1}^{n}(obs_i-\bar{obs})^2}}.$$
NRMSE is unitless and zero is ideal. Smaller values indicate less error
relative to the observed variation. A value of one means RMSE equals one
observed sample standard deviation. This package uses this normalization to
remain consistent with its diagram statistics. It returns NA with a
warning when fewer than two valid pairs remain or the observations have zero
variance. Missing-value handling follows bias().
References
Taylor, K. E. (2001). Summarizing multiple aspects of model performance in a single diagram. Journal of Geophysical Research, 106, 7183-7192. doi:10.1029/2000JD900719
Examples
nrmse(1:3, c(1, 3, 2))
#> [1] 0.8164966