Issue 76: Add weibull distribution to analytic solutions in vignette

[SamuelBrand1]

Description

This PR adds the Weibull distribution to the analytic solutions currently in "Why it works" vignette, following the same pattern as the Log-Normal and the Gamma.

This PR closes #76 .

Checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have included the target issue or issues in the PR title in the for Issue(s) issue-numbers: PR title
• I have read the contribution guidelines.
• I have tested my changes locally.
• I have added or updated unit tests where necessary.
• I have updated the documentation if required.
• My code follows the established coding standards.
• I have added a news item linked to this PR.
• I have reviewed CI checks for this PR and addressed them as far as I am able.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.76%. Comparing base (df08644) to head (a4d5a21).
Report is 1 commits behind head on main.

Additional details and impacted files

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  Misses          1        1           

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[seabbs]

This looks great. I think we (and I certainly needed this) need some more stepping stones in 3.11. In particular, the target integral in full, why the substitution and then how that allows you to solve.

[SamuelBrand1]

I've done a few more steps as well as describing the basic inspiration.

Found a few typos in the intermediate steps as well so good to catch those.

[seabbs]

Looks like it needs a spell check

[seabbs]

/update-wordlist

[seabbs]

/update_wordlist

[seabbs]

Really helpful signposting. Looking forward to implementing this.