Created
August 5, 2009 12:17
-
-
Save naoyat/162659 to your computer and use it in GitHub Desktop.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
(use math.const) ;; pi | |
(define *epsilon* 1e-12) | |
;; | |
;; normal quantile function (probit function) | |
;; | |
(define (probit p) | |
(define (probit>0 p) | |
(* (inverse-erf (- (* p 2) 1)) (sqrt 2))) ;; OK | |
(if (< p 0) | |
(- 1 (probit>0 (- p))) | |
(probit>0 p) )) | |
(define (probit p) | |
(define (probit>0 p) | |
(* (sqrt 2) (inverse-erf (- (* p 2) 1)))) ;; NG | |
(if (< p 0) | |
(- 1 (probit>0 (- p))) | |
(probit>0 p) )) | |
;; | |
;; inverse error function (erf-1) | |
;; | |
(define (inverse-erf z) | |
(define (calc-next-ck k c) | |
(let loop ((m 0) (sum 0) (ca c) (cz (reverse c))) | |
(if (= m k) sum | |
(loop (+ m 1) | |
(+ sum (/. (* (car ca) (car cz)) (+ m 1) (+ m m 1))) | |
(cdr ca) (cdr cz))))) | |
(define (calc-cks k) | |
(let loop ((i 0) (cks '(1))) | |
(if (= i k) cks | |
(loop (+ i 1) (cons (calc-next-ck (+ i 1) cks) cks))))) | |
(define (calc-ck k) (car (calc-cks k))) | |
(define (inverse-erf>0 z) | |
(let1 r (* pi z z 1/4) ; (πz^2)/4 | |
(let loop ((k 0) (cks '(1)) (sum 0) (a 1)) | |
(let1 delta (* a (/ (car cks) (+ k k 1))) | |
(if (< delta (* sum *epsilon*)) | |
(* 1/2 z (sqrt pi) sum) | |
(loop (+ k 1) | |
(cons (calc-next-ck (+ k 1) cks) cks) | |
(+ sum delta) | |
(* a r))))))) | |
(cond [(< z 0) (- (inverse-erf>0 (- z)))] | |
[(= z 0) 0] | |
[else (inverse-erf>0 z)]) ) | |
;; | |
;; TEST | |
;; | |
(use gauche.test) | |
(test-start "erf") | |
(test-section "probit function") | |
(define ~= (lambda (x y) (< (abs (- x y)) 1e-7))) | |
(test* "probit(0.025)" -1.959964 (probit 0.025) ~=) | |
(test* "probit(0.975)" 1.959964 (probit 0.975) ~=) | |
(test-end) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment