Tail dependence bounds

[Alastair_in_SA]

I was just looking over the tail dependence bounds of the various Archimedean copulas, and I noticed that the tail dependence formula for the Gumbel copula (given by Sweeting) does not lie between 0 and 1. This is surely an error?

Sweeting gives the upper tail dependence of a Gumbel copula as:

2 - 2^(-1 / alpha)

If alpha had to equal 2, say, then the upper tail dependence is:

2 - 2^(-1/2) > 1

Is the formula supposed to read:

2 - 2^(1 / alpha)

i.e. no negative in the exponent?

Thanks a lot

 

[td290]

I was just looking over the tail dependence bounds of the various Archimedean copulas, and I noticed that the tail dependence formula for the Gumbel copula (given by Sweeting) does not lie between 0 and 1. This is surely an error?

Sweeting gives the upper tail dependence of a Gumbel copula as:

2 - 2^(-1 / alpha)

If alpha had to equal 2, say, then the upper tail dependence is:

2 - 2^(-1/2) > 1

Is the formula supposed to read:

2 - 2^(1 / alpha)

i.e. no negative in the exponent?

Thanks a lot

See posts #14 to #16:

http://www.acted.co.uk/forums/showthread.php?t=5500&page=2

 

[Alastair_in_SA]

Thank you very much. I thought I couldn't have been the first to notice that. The linked thread seems a good source to consult before adding another thread in future.