I wonder if there is a quantile function for t-distribution, similar to inv_Phi(). If not, is there any trick that I can use to generate such a quantile function? Thanks!

There is nothing in Stan. The best algorithm is probably in section 3 of 0901.0638.pdf 1344.43 KB

Thanks! Looks complicated … [image] This may be silly, but Is it possible for me to define such a function in Stan, by taking advantage of integrate_id() and gamma()?

Yes, and algebraic_solver if you need the inverse CDF.

I tried algebra_solver to get inverse CDF of t distribution functions{ vector algebra_system(vector y, vector theta, real[] x_r, int[] x_i){ vector[1] solution; solution[1] = student_t_cdf(y[1], theta[1], 0, 1) - theta[2]; return solution; } } data { … } transformed data { vector[1] y_gu…

I wrote an implementation of the algorithm Ben Goodrich linked above here: GitHub - szego/truncated-student-t-rng The function n_t_q(z, nu) defined in this Stan code is an approximation for F_inv(G(z)), where G is the CDF of the standard normal distribution and F_inv(p) is the quantile function for…

Student T cumulative distribution function

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spinkney February 2, 2024, 8:33pm 10

Cool! I also coded up the R student t qf in Stan last year. It’s at Student_t quantile function if you want to test it as well.

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Student T cumulative distribution function

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