Logprob derivation of Min for Discrete IID distributions

[Dhruvanshu-Joshi]

What is this PR about?
This PR is the extension of PR 6790 and aims to provide a solution for implementing the Min operation for discrete distributions from order statistics to solve the issue 6350 and issue 6773.

CC: @larryshamalama @ricardoV94

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📚 Documentation preview 📚: https://pymc--6968.org.readthedocs.build/en/6968/

[codecov]

Codecov Report

Attention: 3 lines in your changes are missing coverage. Please review.

Comparison is base (7bb2ccd) 92.21% compared to head (829b63c) 83.57%.
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6968      +/-   ##
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- Coverage   92.21%   83.57%   -8.64%     
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  Files         101      101              
  Lines       16912    16937      +25     
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- Hits        15595    14155    -1440     
- Misses       1317     2782    +1465     

Files	Coverage Δ
pymc/logprob/order.py	98.13% <95.23%> (+2.80%)	⬆️
pymc/logprob/transforms.py	95.73% <90.00%> (-0.15%)	⬇️
pymc/logprob/utils.py	97.20% <94.11%> (-0.42%)	⬇️

... and 19 files with indirect coverage changes

[ricardoV94]

Maybe a good test for discrete would be min/max(Bernoulli)?

def test_min_max_bernoulli():
    p = 0.7
    q = 1 - p
    n = 3
    x = pm.Bernoulli.dist(p=p, shape=(n,))
    value = pt.scalar("value", dtype=int)

    max_logp_fn = pytensor.function([value], pm.logp(pt.max(x), value))
    np.testing.assert_allclose(max_logp_fn(0), np.log(q ** n))
    np.testing.assert_allclose(max_logp_fn(1), np.log(1 - q ** n))

    min_logp_fn = pytensor.function([value], pm.logp(pt.min(x), value))
    np.testing.assert_allclose(min_logp_fn(1), np.log(p ** n))
    np.testing.assert_allclose(min_logp_fn(0), np.log(1 - p ** n))

This suggests @larryshamalama implementation is correct. I guess I was tripped by the cdf for discrete variables being P(X<=x) and not P(X<x)

[Dhruvanshu-Joshi]

The test "test_discrete_rv_multinary_transform_fails():" as it should.
https://github.com/Dhruvanshu-Joshi/pymc/blob/4d2ac0d8f57620e00788f2f3c0d1184109b184fc/tests/logprob/test_transforms.py#L1251C1-L1254

[Dhruvanshu-Joshi]

Todo:
Once this is merged, I'll open a seperate PR so that the test for transforms that fails does not do so.

[Dhruvanshu-Joshi]

Hey @ricardoV94 @larryshamalama . I have commited the changes discussed in the last week. Please give it a look as you find the time.

[ricardoV94]

Suggested change

	"min_discrete",
	"min",

[ricardoV94]

Great work @Dhruvanshu-Joshi