Which of the following is an Archimedean copula over two distribution functions $F _ { 1 } , F _ { 2 }$ ?
A) $C \left( F _ { 1 } , F _ { 2 } \right) = \ln \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$
B) $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { a } \right\}$
C) $C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}$
D) None of the above.

Question

Quizplus · Accepted Answer

Option C is correct because it represents a form of the Gumbel copula, which is a type of Archimedean copula. The Gumbel copula is defined using an exponential function of a sum of powers, which matches the structure given in option C.

Which of the Following Is an Archimedean Copula Over Two F1,F2F _ { 1 } , F _ { 2 }F1​,F2​

Which of the Following Is an Archimedean Copula Over Two $F _ { 1 } , F _ { 2 }$