Correlation
Pearson correlation
\[\rho_{X, Y}
:=
\frac{
\mathrm{E}
\left[
\left(
X
-
\mathrm{E}
\left[
X
\right]
\right)
\left(
Y
-
\mathrm{E}
\left[
X
\right]
\right)
\right]
}{
\sqrt{
\mathrm{E}
\left[
\left(
X
-
\mathrm{E}
\left[
X
\right]
\right)^{2}
\right]
\mathrm{E}
\left[
\left(
Y
-
\mathrm{E}
\left[
Y
\right]
\right)^{2}
\right]
}
}\]
Spearman correlation
Kendall correlation
Reference