docs: add doctest examples for correlation classes

[priyam0k]

Adds Sphinx doctest Examples sections to the DevelopmentCorrelation and ValuationCorrelation classes.

Refs #704 (Development Pattern Estimators → DevelopmentCorrelation and ValuationCorrelation rows).

Summary of Changes

• Adds an Examples block to DevelopmentCorrelation in chainladder/core/correlation.py.
• Adds an Examples block to ValuationCorrelation in the same file.
• Each block opens with the Mack chain-ladder assumption being tested, then exercises the decision the user actually makes.

DevelopmentCorrelation example:

• Runs on the RAA sample.
• Prints t_expectation, both ends of confidence_interval, and the t_critical boolean — so the reader sees 0.0696 sitting inside (-0.1275, 0.1275) and understands why the test does not reject independence.

ValuationCorrelation example:

• One testcode block for total=False (Mack 1997) printing the per-diagonal z_critical matrix.
• A second testcode block for total=True (Mack 1993) printing the whole-triangle z and boolean (14.0, False).
• One-line interpretation tying each result back to the chain-ladder workflow.

All numeric outputs use round(float(...), 4) (same pattern as #836) so the doctest is stable across numpy versions and array backends. Docstring-only; no runtime logic or public API changes.

Related GitHub Issue(s)

• Refs API Reference Examples #704
• Follows the conventions used in DOCS: Expand Triangle constructor examples (#704) #714, DOCS: Add examples to Triangle methods and properties (#704) #719, and docs: add BootstrapODPSample doctest examples #836.

Additional Context for Reviewers

• Doctest CI passed locally.

• pytest chainladder/core/tests -x -q → no regressions.

• Drafted against the four-point rubric @henrydingliu posted on API Reference Examples #704 / More robust PR template and contributing guidelines #827: each example opens with a practical chain-ladder assumption check, stays consistent with Mack 1993 / 1997, points to the existing Mack section of the user guide rather than duplicating it, and prints the full decision signal (statistic, confidence band, boolean) rather than a single boolean.

• Intentionally excludes .github/workflows/sync-main-to-docs.yml, matching the split-PR convention from docs: add tail estimator doctest examples #801 and docs: add BootstrapODPSample doctest examples #836.

• Happy to also embed a worked MackChainladder call inside the example if reviewers want the chain-ladder tie-in to be more concrete — left out here to keep the PR small.

• I passed tests locally for both code (uv run pytest) and documentation changes (uv run jb build docs --builder=custom --custom-builder=doctest)

---

Note

Low Risk
Docstring and doctest narrative only; no executable code or API behavior changes.

Overview
Documentation only for ValuationCorrelation in correlation.py: the Sphinx Examples section is tightened so the opening text no longer mixes per-diagonal and whole-triangle modes in one sentence.

A short bridge paragraph now introduces the second doctest block, explaining that the same calendar-effect check can run as per-diagonal (total=False, Mack 1997) or whole-triangle (total=True, Mack 1993) before the existing total=True example that prints aggregated z and z_critical.

No changes to correlation logic, parameters, or public API—only how reviewers read the worked examples.

^{Reviewed by Cursor Bugbot for commit 3d827d9. Bugbot is set up for automated code reviews on this repo. Configure here.}

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.94%. Comparing base (6ea3577) to head (3d827d9).
⚠️ Report is 221 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #844      +/-   ##
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+ Coverage   85.12%   86.94%   +1.81%     
==========================================
  Files          85       86       +1     
  Lines        4909     4994      +85     
  Branches      629      644      +15     
==========================================
+ Hits         4179     4342     +163     
+ Misses        521      462      -59     
+ Partials      209      190      -19     

Flag	Coverage Δ
unittests	86.94% <ø> (+1.81%)	⬆️

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[henrydingliu]

can move this line between per-diagonal test and total test

[priyam0k]

Good catch, moving it between the two blocks so the intro stays scoped to the concept and the total=True form is introduced where it actually runs. Pushed as 3d827d9.

[henrydingliu]

thanks for putting this together. there's actually no longer any examples with developmentcorrelation in the doc. so this was much needed. just one small nitpick