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ManuelAlvarezC avatar ManuelAlvarezC commented on June 4, 2024

This has been mostly implemented on the branch 46_independence_bivariate_copula. However there is an implementation detail that should be discussed before merging it:

In the case of independent random variables, the cumulative_distribution is just the product of the two variables. For this reason, the percent_point, which is the reverse of the cumulative_distribution can have multiple outputs, as for a given y in [0,1], there are infinite values u, vthat fulfill C(u,v) = y.

Some examples:

C(1, y) = y
C(y, 1) = y
C(y ** 1 / 2, y ** 1 / 2) = y
C(x, y / x) = y  #  ( in this case for any x != 0)

Should we pick one option or leave it unimplemented?

What do you think @aliciasun @csala ?

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ManuelAlvarezC avatar ManuelAlvarezC commented on June 4, 2024

There was a misunderstanding in my last post.

The percent_point method in Bivariate copulas is not the inverse of cumulative_distribution but the inverse of conditional_probability.
With that in mind, we can solve the question easily, because the conditional_probability of an independence copulas is the identity, and its inverse is also the identity.

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