Updated Mack's sigma_interpolation to use "mack"

[henrydingliu]

Summary of Changes

Changing interpolation approach to match paper

Related GitHub Issue(s)

closes #1093

Additional Context for Reviewers

• 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
Changes are limited to a documentation notebook example; no library code paths are modified in this diff.

Overview
Updates the MackChainladder gallery notebook so the worked example uses Development(sigma_interpolation='mack') instead of Development(average='volume'), aligning Mack standard errors and ultimates with Mack (1994) (page 130 figures).

Also fixes a typo in the intro markdown (“can can” → “can”) and expands comments to describe the Mack interpolation choice.

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[github-actions]

Pyright Type Completeness

View the full pyright --verifytypes output for this commit

Project (full chainladder package, at this PR's head): 15.0% of exported symbols fully typed (196 / 1305)

	Known	Ambiguous	Unknown	Total
Project (head)	196	110	999	1305

Other symbols referenced but not exported by chainladder: 13

	Known	Ambiguous	Unknown	Total
Other (head)	3	1	9	13

Symbols without documentation:

• Functions without docstring: 315
• Functions without default param: 0
• Classes without docstring: 10

Patch (exported symbols added or changed by this PR): no exported symbol type-completeness changes detected.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.14%. Comparing base (bb16128) to head (a4c34c6).

Additional details and impacted files

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  Coverage   91.14%   91.14%           
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  Files          91       91           
  Lines        5365     5365           
  Branches      681      681           
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  Hits         4890     4890           
  Misses        340      340           
  Partials      135      135           

Flag	Coverage Δ
unittests	91.14% <ø> (ø)

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[kennethshsu]

Updated the PR title.

Let me dismiss this

[kennethshsu]

@priyam0k do you want to take a look at this?

[priyam0k]

thanks for the ping @kennethshsu.

change looks right to me. average='volume' is already the default, so the ldfs are unchanged and the only thing moving is sigma, from log-linear to mack. that also lines up with test_mack1994_hardcode in test_mack.py, which fits Development(sigma_interpolation='mack') on raa and reconciles to the same p130 tables, so the gallery example now matches what the test already asserts.

one thing to fix in the same PR: the intro markdown at the top still says "this example does not fully reconcile to the original paper due to the default usage of log-linear sigma interpolation". after this change it does reconcile, so that note is now wrong.

otherwise lgtm.

[henrydingliu]

the intro markdown at the top still says "this example does not fully reconcile to the original paper due to the default usage of log-linear sigma interpolation".

where are you seeing this?

[priyam0k]

my mistake, that line's actually on experimental (9dcebfb), not main, so it doesn't apply here. sorry for the mix-up. i did notice a tiny typo in main's intro ("can can") line 30, nothing urgent,