Create inverse_scaled_logistic_saturation and the corresponding class

[arthurmello]

Description

Offer a more intuitive alternative to logistic_saturation, where we use
$$f(x,λ)=\frac{1−e^{−xln⁡(3)/λ}}{1+e^{−xln⁡(3)/λ}}$$

Instead of the original:
$$f(x,λ)=\frac{1−e^{−xλ}}{1+e^{−xλ}}$$

Allowing for lambda to be interpreted as the half saturation point.

Related Issue

• Closes #
• Related to Proposal: Use a more intuitive parametrization of logistic_saturation #220

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Modules affected

• MMM
• CLV

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

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📚 Documentation preview 📚: https://pymc-marketing--827.org.readthedocs.build/en/827/

[wd60622]

Amazing stuff. Thanks for this contribution!

Can you test that the tranformation at lam is about 0.5? It should be test in transformations.py

[wd60622]

add that this results in halfway saturation at lam

[arthurmello]

@wd60622 I've updated the PR with those changes, let me know if there's anything else I can do :)

[wd60622]

One final request ☺️

[wd60622]

Looks good! Just running tests one last time

[wd60622]

Thanks @arthurmello !