Issue 85: Analytical solutions in stan

[seabbs]

Description

This PR closes #85 by adding analytical solutions in stan and tests to compare them to R side solutions.

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 (345e95b) to head (aaf7663).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #95   +/-   ##
=======================================
  Coverage   99.76%   99.76%           
=======================================
  Files          10       10           
  Lines         423      427    +4     
=======================================
+ Hits          422      426    +4     
  Misses          1        1           

Flag	Coverage Δ
	99.76% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[seabbs]

LGTM (self-review)

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if aaf7663 is merged into main:

• ✔️cmdstan_fit_gamma_expgrowth: 7.67s -> 7.66s [-0.82%, +0.38%]
• 🚀cmdstan_fit_lognormal_unif: 1.66s -> 751ms [-58.21%, -51.2%]
• ❗🐌dprimarycensoreddist_pweibull_expgrowth: 2.37ms -> 2.44ms [+0.27%, +5.3%]
• ❗🐌dprimarycensoreddist_weibull: 2.31ms -> 2.37ms [+0.41%, +4.19%]
• ✔️fitdistdoublecens_gamma_expgrowth: 663ms -> 662ms [-0.62%, +0.31%]
• ✔️fitdistdoublecens_normal: 551ms -> 551ms [-0.26%, +0.24%]
• ❗🐌pprimarycensoreddist_lnorm: 1.9ms -> 2ms [+3.41%, +7.32%]
• ✔️pprimarycensoreddist_plnrom_expgrowth: 48.1ms -> 48.4ms [-1.07%, +2.03%]
  Further explanation regarding interpretation and methodology can be found in the documentation of touchstone.