27.18 ERA 3.3 Modeling and Dependency: Correlations and Copulas - G. Venter

\(\star\) Correlation

Pearson’s correlation:

• Formula (24.1)

Kendall’s \(\tau\):

• Formula (24.2) for discrete and continuous (24.3) & (24.4)

Copulas

Using copula and Sklar’s Theorem 24.1

• Joint density function express with copula (24.5)

Properties of the main copulas in table 24.1 and the partial perfect correlation copula

• Simulation for each of the copula Frank, Gumble, HRT is same as Frank, and Normal

  • Gumbel’s formula (24.15) & (24.16)

Tail Concentration Functions

Left tail and right tail concentration function for each copulas 24.1