Probit Function in Racket. This gives quantiles of the standard normal, which ends up being trickier to implement than you might guess. We follow the "quantile mechanics" approach of Steinbrecher and Shaw: http://www.homepages.ucl.ac.uk/~ucahwts/lgsnotes/EJAM_Quantiles.pdf.

probit.rkt

#lang racket

(define (sum-to n term)
  (letrec ((S (lambda (acc k)
                (cond
                  [(eq? k 0) (+ (term 0) acc)]
                  [else (S (+ acc (term k)) (- k 1))]))))
    (S 0.0 n)))
                  
(define vs '())
(define lookup
  (lambda (v)
    (cdr (assoc v vs))))

(define extend
  (lambda (k v)
    (set! vs (cons (cons k v)
                   vs))))

(define (W k)
  (cond
    [(eq? k 0) 1.0]
    [(assoc k vs) (lookup k)]
    [else
     (let ([new-v (* (/ pi 4.0)
                     (sum-to (- k 1) (lambda (j) (/ (* (W j) (W (- k (+ j 1))))
                                                    (* (+ j 1) (+ (* 2 j) 1))))))])
       (extend k new-v)
       new-v)]))

(define probit
  (lambda (p)
    (letrec ((S (lambda (acc k)
                  (cond
                    [(eq? k 0) (* (+ acc (* (/ (W 0)
                                               (+ (* 2 0) 1))
                                            (expt (- (* 2 p) 1)
                                                  (+ (* 2 0) 1))))
                                  (sqrt (/ pi 2)))]
                    [else
                     (S (+ acc (* (/ (W k)
                                     (+ (* 2 k) 1))
                                  (expt (- (* 2 p) 1)
                                        (+ (* 2 k) 1))))
                        (- k 1))]))))
      (S 0.0 100))))