;;; PLT Scheme Science Collection
;;; random-distributions/chi-squared.ss
;;; Copyright (c) 2004-2006 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 chi-squared distribution.  It is based
;;; on the Ranfom 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)
;;; 1.1.0    02/08/06  Added cdf.  (Doug Williams)

(module chi-squared mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-chi-squared
    (case-> (-> random-source? real? (>=/c 0.0))
            (-> real? (>=/c 0.0))))
   (chi-squared-pdf
    (-> real? real? (>=/c 0.0)))
   (chi-squared-cdf
    (-> real? real? (real-in 0.0 1.0))))
  
  (require "../random-source.ss")
  (require "../special-functions/gamma.ss")
  (require "gamma.ss")
  
  ;; random-chi-squared: random-source x real -> real
  ;; This function returns a random variate from the chi-squared
  ;; distribution with nu degrees of freedom.
  (define random-chi-squared
    (case-lambda
      ((r nu)
       (* 2.0 (random-gamma r (/ nu 2.0) 1.0)))
      ((nu)
       (random-chi-squared (current-random-source) nu))))
  
  ;; chi-squared-pdf: real x real -> real
  ;; This function computes the probability density p(x) at x for the
  ;; chi-squared distribution with nu degrees of freedom.
  (define (chi-squared-pdf x nu)
    (if (<= x 0.0)
        0.0
        (let ((lngamma-val (lngamma (/ nu 2.0))))
          (/ (exp (- (* (- (/ nu 2.0) 1.0)
                        (log (/ x 2.0)))
                     (/ x 2.0) lngamma-val))
             2.0))))
  
  ;; chi-squared-cdf: real x real -> real
  ;; This function computes the cummulative density d(x) at x for the
  ;;; chi-squared distribution with nu degrees of freedom.
  (define (chi-squared-cdf x nu)
    (gamma-cdf x (/ nu 2.0) 2.0))
  
)