Statistics

The Root-Mean-Squared Error is defined as

$RMSE={\sqrt {{\bigg \langle }{\big (}x-y{\big )}^{2}{\bigg \rangle }}}$

(1)

The Relative-Mean-Absolute Error is defined as

$RMAE={\frac {{\bigg \langle }{\big |}x-y{\big |}{\bigg \rangle }}{{\big |}x{\big |}}}$

(2)

The correlation coefficient is defined as

$R={\frac {\langle xy\rangle -\langle x\rangle \langle y\rangle }{{\sqrt {\langle x^{2}\rangle -\langle x\rangle ^{2}}}{\sqrt {\langle y^{2}\rangle -\langle y\rangle ^{2}}}}}$

(3)

The bias is given by

$B=\langle x\rangle -\langle y\rangle$

(4)