Issue 125: Update analytic solutions to deal with possible neg t values

[SamuelBrand1]

Description

This PR closes #125 .

I've gone back through the maths to grab occasions where the full representation of the pdf of a distribution (including the zero value for negative arg branch) is needed to get the correct answer.

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.
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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.35%. Comparing base (2a55442) to head (5684533).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #126   +/-   ##
=======================================
  Coverage   99.35%   99.35%           
=======================================
  Files          10       10           
  Lines         463      463           
=======================================
  Hits          460      460           
  Misses          3        3           

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[seabbs]

phew - nice!