Student t large n

[Beakerboy]

Translated C code from R. Need to go over it, but looks promising.
The new test cases do not appear in the current develop branch.

[Beakerboy]

#429

Potential patch. Currently a hack job at best.

• May need to create a logGamma function
• Double check the values of defined constant, epsilon, log_pi, etc.
• Fix the one failure t = 0, v = 6.

[Beakerboy]

WOW! All the high df tests pass!
Only three failures:
t=0 df = 6
t=±2 df = 20

[coveralls]

Coverage increased (+0.002%) to 99.934% when pulling 98387a3 on Beakerboy:StudentT_Large-n into cb4a396 on markrogoyski:develop.

[Beakerboy]

Need the following test cases:

• df > 1000
• Huge t²/v
• stirlerr for non 1/2 integers. This section of code will not execute in T...cut it out?

[markrogoyski]

            [0, 500, 0.3987429],
            [1, 500, 0.241729],
            [2, 500, 0.05417883],
            [3, 500, 0.004569562],
            [5, 500, 1.962337e-06],

            [0, 1000, 0.3988426],
            [1, 1000, 0.2418498],
            [2, 1000, 0.05408517],
            [3, 1000, 0.004500625],
            [5, 1000, 1.712012e-06],

            [0, 1200, 0.3988592],
            [1, 1200, 0.2418699],
            [2, 1200, 0.05406951],
            [3, 1200, 0.004489151],
            [5, 1200, 1.672771e-06],

            [0, 1500, 0.3988758],
            [1, 1500, 0.2418901],
            [2, 1500, 0.05405383],
            [3, 1500, 0.004477681],
            [5, 1500, 1.634218e-06],

[Beakerboy]

And there was much rejoicing....

[markrogoyski]

I don't understand any of it...but the tests pass =)

[Beakerboy]

It's black magic to me too.

[Beakerboy]

This appears to be the source of the algorithm:
https://www.r-project.org/doc/reports/CLoader-dbinom-2002.pdf