How to create my own table for student's t distribution?

Question

I'm trying to compute the values of a student's t distribution, but I don't get how is it calculated. I need something like

$$ P(T<t)=t_{n,\alpha} $$

but im not sure where does the parameter $\alpha$ enters in this coputation, $\alpha$ is the parameter for the confidence level $1-\alpha$ and $n$ is the number of degrees of freedom.

Answer 1

As to why you may experience some difficulties computing the values for the Student's t-distribution, some background comments from Wikipedia on the topic of the quantile function (inverse of the CDF), to quote:

The evaluation of quantile functions often involves numerical methods...Quantile functions may also be characterized as solutions of non-linear ordinary and partial differential equations. The ordinary differential equations for the cases of the normal, Student, beta and gamma distributions have been given and solved.[4]

And further:

Student's t-distribution (further information: Student's t-distribution)

This has historically been one of the more intractable cases, as the presence of a parameter, ν, the degrees of freedom, makes the use of rational and other approximations awkward. Simple formulas exist when the ν = 1, 2, 4 and the problem may be reduced to the solution of a polynomial when ν is even. In other cases the quantile functions may be developed as power series.[8]

My advice, get good technical support as this has been described as 'one of the more intractable cases', but with special exceptions.