DOCS: Add examples to deterministic IBNR methods (#704)

[EKtheSage]

What does this pull request do?

Addresses #704 for the deterministic IBNR estimator classes (the third tranche after #714 for the Triangle constructor and #719 for Triangle methods/properties).

Adds doctest-validated Examples blocks to the five deterministic estimator classes, matching the same Polars-style format established in #714 and #719: no import statements, ... continuation prefixes, strict output indentation, and byte-exact output with no NORMALIZE_WHITESPACE flag.

Coverage

File	Blocks	What was added
chainladder.py	3	Class docstring Examples, fit, predict
mack.py	8	Class Examples, fit, predict (full new docstring — none existed before), plus full docstrings for the five Mack-specific properties: full_std_err_, total_process_risk_, mack_std_err_, total_mack_std_err_, summary_
bornferg.py	3	Class Examples, fit, predict
benktander.py	3	Class Examples, fit, predict
capecod.py	3	Class Examples, fit, predict

Total: 20 doctest blocks.

Teaching points worth flagging

• BornhuetterFerguson class docstring documents the canonical cl_ult * 0 + value idiom for constructing a flat per-origin apriori. sample_weight must be a chainladder Triangle, not a scalar; passing sample_weight=14000 raises AttributeError. New users hit this constantly.
• Benktander class docstring shows side-by-side that n_iters=1 reproduces Bornhuetter-Ferguson and increasing n_iters pulls the ultimates toward the chainladder estimate.
• CapeCod class docstring contrasts the role of sample_weight (exposure here, vs. apriori expected ultimate in BF/Benktander) and shows the effect of trend and decay on the derived apriori_.
• MackChainladder.total_mack_std_err_ docstring notes that the across-origin total exceeds the quadrature sum of per-origin mack_std_err_ because parameter risk is correlated across origins (each origin uses the same estimated age-to-age factors).

Out of scope

Inherited methods from sklearn (get_params, set_params, get_metadata_routing, set_fit_request, set_predict_request) and from chainladder mixins (intersection, set_backend, to_json, to_pickle, plus the Common properties ibnr_, full_triangle_, full_expectation_, ldf_, latest_diagonal) are not documented here. The mixin methods are shared across many subclasses and warrant their own follow-up PR.

Validation

All 20 example blocks were executed with Python's doctest module in strict mode (no NORMALIZE_WHITESPACE flag) and pass with byte-exact output comparison.

Relevent Github ticket(s)?

Issue #704. Companion to PRs #714 (constructor) and #719 (Triangle methods/properties).

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Note

Low Risk
Documentation-only changes that add doctest-validated examples to several actuarial estimators; primary risk is brittle doctest output expectations affecting CI, with no runtime logic changes.

Overview
Adds doctest-validated Examples documentation to the deterministic IBNR estimators Chainladder, BornhuetterFerguson, Benktander, and CapeCod, covering typical fit/predict workflows and key attributes like ultimate_, ibnr_, and apriori_.

Expands MackChainladder docs with new predict documentation and detailed example blocks for Mack-specific outputs (full_std_err_, total_process_risk_, mack_std_err_, total_mack_std_err_, summary_).

^{Reviewed by Cursor Bugbot for commit 37beb69. 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 85.12%. Comparing base (6ea3577) to head (37beb69).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #721   +/-   ##
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  Coverage   85.12%   85.12%           
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  Files          85       85           
  Lines        4909     4909           
  Branches      629      629           
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  Hits         4179     4179           
  Misses        521      521           
  Partials      209      209           

Flag	Coverage Δ
unittests	85.12% <ø> (ø)

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