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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) =yC(y, 1) =yC(y**1/2, y**1/2) =yC(x, y/x) =y# ( in this case for any x != 0)
Should we pick one option or leave it unimplemented?
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.
Description
Add a independence copula class to fit data that are not correlated.
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