Gaussian copula

[Ben Abbott]

On May 4, 2008, at 10:25 AM, Dorian wrote:
>
>> 2008/4/4 Ben Abbott <bpabbott at mac.com>:
>>
>> On Apr 3, 2008, at 11:44 AM, Dorian wrote:
>> hi all,
>>
>> Is there a simple way to plot a gaussian copula with octave ?
>>
>> Any hint will be very appreciated
>>
>> Thanks in advance
>>
>> In the event you're looking for a function to calculate the curve,  
>> there is one at the link below.
>>
>>        http://www.koders.com/matlab/fid26069CC4A023DEC477427496F77F5EB8A2A8412C.aspx
>>
>> You'll need the following function also.
>>
>>        http://www.koders.com/matlab/fid950678C6674B791F9548A1595C8CFC013A3F7FFC.aspx
>>
>> An example is below,
>>
>> u = linspace(0.01,0.99,101);
>> v = u;
>> alpha = 0.5;
>>
>> [u, v] = meshgrid (u, v);
>>
>> z = copulapdf ('gaussian', u, v, alpha);
>>
>> mesh (u, v, z)
>> xlabel ("u")
>> ylabel ("v")
>> zlabel ("copula")
>
> hello,
>
> I had used all the link you sent, and  I got many nice plot  for  
> different copula densities .
>
> Now I am dealing with matrices U and V which have entries 0 and 1.
> Is there a simple way to plot in that case the copula densities say   
> c(U,V) , depend on U and V.
>
> How could I set "alpha" .
> I'm getting error of size when  "alpha"  as an array according to  
> the range of copula .
>
> Thanks ,

I'm not familiar with these functions, or the underlying algorithms.,  
but it appears the help provided by the function answers your questions.

 > help  copulapdf

    FUNCTION C = COPULAPDF(FAMILY, U, ALPHA)

    Return c(u,v|ALPHA), the copula density.

    INPUTS
        FAMILY: one of {'ind', 'gaussian', 'gumbel' 'clayton' 'frank'  
'amh' 'joe' 'fgm' 'arch12' 'arch14'}
        U: Nx2 vector (u,v) in [0,1]^2.
        ALPHA: 1xM vector of copula parameters
            or
    COPULAPDF(FAMILY, U1, U2, ALPHA)
        U1, U2:  Matrices or row vectors.
                 If U1 is (1xN) and U2 is (1xM), c is (NxM)
                 If U1 is (NxM), U2 must be (N,M).
        ALPHA:   Scalar copula parameter

    OUTPUT
        C:       Copula density c(u,v|ALPHA) (NxM).

So if I've inferred what you're hoping to do, try

u = linspace(0.01,0.99,101);
v = linspace(0.01,0.99,101);

% the 2nd input contains both u & v
U = [u(:), v(:)];
% I don't know what a reasonable range for alpha is, but I'll try 0 to 1
alpha = linspace(0,1,11);
z = copulapdf ('gaussian', U, alpha);

[x, y] = meshgrid (alpha, u);
mesh (x, y, log10(z))
xlabel("Alpha")
ylabel("u")

There is no need for "u" and "v" to be identical, but they do need to  
be the same length.

Ben