Compute critical value T-Score using Math.NET

Question

Any thoughts on how I can compute critical value in a t-distribution using Math.NET?

More concretely, I am looking for how to compute the following excel function using Math.NET.

=T.INV.2T(0.05, 8)

Answer 1

How about

var x = MathNet.Numerics.Distributions.StudentT.InvCDF(location:0.0, scale:1.0, freedom: (double)8, p: 0.05);

You should check against T.INV.2T whether two-tailed value is returned, if not just adjust the probability

You could also compare with critical values here

UPDATE

C# code below (.NET Core 3.1, Math.NET v4.9, Win10 x64)

using System;
using MathNet.Numerics.Distributions;

namespace Tinv
{
    class Program
    {
        public static double T_INV_2T(double p, double nu)
        {
            return StudentT.InvCDF(location:0.0, scale:1.0, freedom: nu, p: 1.0 - p/2.0);
            // same as             return Math.Abs(StudentT.InvCDF(location:0.0, scale:1.0, freedom: nu, p: p/2.0));

        }

        static void Main(string[] args)
        {
            var x = T_INV_2T(0.05, (double)8);
            Console.WriteLine($"Output = {x}");
        }
    }
}

produced output

2.306004135204172

where Excel produced value of =T.INV.2T(0.05, 8) equal to 2.306004, and in the NIST table by the link value is listed as 2.306

Seems quite consistent