Statistics

The Root-Mean-Squared Error is defined as

$RMSE=\sqrt{⟨(x-y{)}^2⟩}$

(1)

The Relative-Mean-Absolute Error is defined as

$RMAE=\frac{⟨|x-y|⟩}{\left|x\right|}$

(2)

The correlation coefficient is defined as

$R=\frac{⟨xy⟩-⟨x⟩⟨y⟩}{\sqrt{⟨x^2⟩-⟨x{⟩}^2}\sqrt{⟨y^2⟩-⟨y{⟩}^2}}$

(3)

The bias is given by

$B=⟨x⟩-⟨y⟩$

(4)