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Add independence bivariate class #46

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aliciasun opened this issue Aug 14, 2018 · 2 comments · Fixed by #94
Closed

Add independence bivariate class #46

aliciasun opened this issue Aug 14, 2018 · 2 comments · Fixed by #94
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@aliciasun
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Description

Add a independence copula class to fit data that are not correlated.

@aliciasun aliciasun added this to the 0.2.0 milestone Aug 14, 2018
@aliciasun aliciasun added the feature request Request for a new feature label Aug 14, 2018
@aliciasun aliciasun changed the title Add independence copula Add independence bivariate class Aug 14, 2018
@aliciasun aliciasun self-assigned this Aug 14, 2018
@ManuelAlvarezC ManuelAlvarezC modified the milestones: 0.2.0, 0.2.1 Aug 21, 2018
@ManuelAlvarezC ManuelAlvarezC modified the milestones: 0.2.1, 0.2.2 Nov 19, 2018
@ManuelAlvarezC
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ManuelAlvarezC commented Mar 14, 2019

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 ?

@ManuelAlvarezC ManuelAlvarezC added the under discussion Issue is currently being discussed label Apr 12, 2019
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ManuelAlvarezC commented Apr 23, 2019

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.

@ManuelAlvarezC ManuelAlvarezC removed the under discussion Issue is currently being discussed label Apr 23, 2019
@csala csala closed this as completed in #94 May 2, 2019
@csala csala assigned ManuelAlvarezC and unassigned aliciasun Jul 31, 2019
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