Implement analytical solutions to PMFs directly in the stan code

[seabbs]

Currently we also drop down to the CDF solutions but there is likely a significant speed up available (due to reducing cdf calls) in directly implementing the analytical solutions for the PMFs.

We should:

• Check the equations to make sure we do indeed expect a speedup
• Implement the PMFs in stan
• unit test PMFs against CDFs

[seabbs]

I think in the first instance we only need to do this for the vectorised helpers as this is where the most obvious speed up will be and its also where performance is most critical.