;;; PLT Scheme Science Collection
;;; random-distributions/t-distribution.ss
;;; Copyright (c) 2004 M. Douglas Williams
;;;
;;; This library is free software; you can redistribute it and/or
;;; modify it under the terms of the GNU Lesser General Public
;;; License as published by the Free Software Foundation; either
;;; version 2.1 of the License, or (at your option) any later version.
;;;
;;; This library is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;; Lesser General Public License for more details.
;;;
;;; You should have received a copy of the GNU Lesser General Public
;;; License along with this library; if not, write to the Free
;;; Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
;;; 02111-1307 USA.
;;;
;;; -------------------------------------------------------------------
;;;
;;; This module implements the t-distribution.  It is based on the
;;; Random Number Distributions in the GNU Scientific Library.
;;;
;;; Version  Date      Description
;;; 1.0.0    09/28/04  Marked as ready for Release 1.0.  Added
;;;                    contracts for functions.  (Doug Williams)

(module t-distribution mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-t-distribution
    (case-> (-> random-source? real? real?)
            (-> real? real?)))
   (t-distribution-pdf
    (-> real? real? (>=/c 0.0))))
  
  (require "../math.ss")
  (require "../random-source.ss")
  (require "../special-functions/gamma.ss")
  (require "gaussian.ss")
  (require "chi-squared.ss")
  (require "exponential.ss")
  
  ;; random-t-distribution: random-source x real -> real
  ;; random-t-distribution: real -> real
  ;;
  ;; This function returns a random-variate from the t-distribution
  ;;; with nu degrees of freedom.
  (define random-t-distribution
    (case-lambda
      ((r nu)
       (if (<= nu 2)
           (let ((y1 (random-unit-gaussian r))
                 (y2 (random-chi-squared r nu)))
             (/ y1 (sqrt (/ y2 nu))))
           (let ((y1 0)
                 (y2 0)
                 (z 0))
             (let loop ()
               (set! y1 (random-unit-gaussian r))
               (set! y2 (random-exponential r (/ 1 (- (/ nu 2) 1))))
               (set! z (/ (* y1 y1) (- nu 2)))
               (if (or (< (- 1 z) 0)
                       (> (exp (- (- y2) z)) (- 1 z)))
                   (loop)))
             (* (/ y2 (sqrt (- 1 (/ 2 nu)))) (- 1 z)))))
      ((nu)
       (random-t-distribution (current-random-source) nu))))
  
  ;; t-distribution-pdf: real x real -> real
  ;;
  ;; This function computes the probability density p(x) at x for a
  ;; t-distribution with nu degrees of freedom.
  (define (t-distribution-pdf x nu)
    (let ((lg1 (lngamma (/ nu 2.0)))
          (lg2 (lngamma (/ (+ nu 1.0) 2.0))))
      (* (/ (exp (- lg2 lg1)) (sqrt (* pi nu)))
         (expt (+ 1.0 (/ (* x x) nu)) (/ (- (+ nu 1.0)) 2.0)))))
  
)