Hi Murielle,
From what I understand, you aim to plot the conditional probability derived from a Gumbel copula given values of Y. First, we can get the copula PDF using the “copulapdf” function which can be utilized as follows:
x = 0:0.1:1;
y=x;
[x, y] = meshgrid(x, y);
gumb_pdf = copulapdf('Gumbel', [x(:), y(:)], 2); % Using 2 as alpha
gumb_pdf = reshape(gumb_pdf, 11, 11);
Then, we can obtain the conditional probabilities by selecting the rows that correspond to the required Y values:
gumb_pdf_y_50 = gumb_pdf(6, :); % Selecting the 6th row for y=0.5
gumb_pdf_y_90 = gumb_pdf(end-1, :); % Selecting the 10th row for y=0.9
Finally, we can visualize the probabilities using “plot”:
plot(0:0.1:1, gumb_pdf_y_50);
hold on;
plot(0:0.1:1, gumb_pdf_y_90);
legend(["Y=0.5", "Y=0.9"], 'Location','northwest');
hold off;
The same can be done with CDFs by using the "copulacdf" function.
I hope this helped.
