#lang scheme/base
;;; PLT Scheme Science Collection
;;; random-distributions/beta.ss
;;; Copyright (c) 2004-2008 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 modules provides the implementation of the beta distribution.
;;; It is based on the Random Number Distributions in the GNU
;;; Scientific Library (GSL).
;;;
;;; 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)
;;; 2.0.0    11/19/07  Added unchecked versions of functions and
;;;                    getting ready for PLT Scheme 4.0 (Doug Williams)
;;; 3.0.0    06/09/08  Changes requred for V4.0.  (Doug Williams)

(require (lib "contract.ss"))

(provide
 (rename-out (random-beta unchecked-random-beta)
             (beta-pdf unchecked-beta-pdf)
             (beta-cdf unchecked-beta-cdf)))

(provide/contract
 (random-beta
  (case-> (-> random-source? real? real?
              (real-in 0.0 1.0))
          (-> real? real?
              (real-in 0.0 1.0))))
 (beta-pdf
  (-> real? real? real? (>=/c 0.0)))
 (beta-cdf
  (-> real? real? real? (real-in 0.0 1.0))))

(require "../random-source.ss")
(require "../special-functions/gamma.ss")
(require "gamma.ss")
(require "cdf-beta-inc.ss")

;;; random-beta: random-source x real x real -> real
;;; random-beta: real x real -> real
;;; These functions return a random variate from the beta distribution
;;; with parameters a and b.
(define random-beta
  (case-lambda
    ((r a b)
     (let ((x1 (unchecked-random-gamma r a 1.0))
           (x2 (unchecked-random-gamma r b 1.0)))
       (/ x1 (+ x1 x2))))
    ((a b)
     (random-beta (current-random-source) a b))))

;;; beta-pdf: real x real x real -> real
;;; This function computes the probability density for the beta
;;; distribution with parameters a and b.
(define (beta-pdf x a b)
  (if (or (< x 0.0)
          (> x 1.0))
      0.0
      (let ((gab (unchecked-lngamma (+ a b)))
            (ga (unchecked-lngamma a))
            (gb (unchecked-lngamma b)))
        (* (exp (- gab ga gb))
           (expt x (- a 1.0))
           (expt (- 1.0 x) (- b 1.0))))))

;;; beta-cdf: real x real x real -> real
;;; This function computes the cummulative probability density for
;;; the beta distribution with parameters a and b.
(define (beta-cdf x a b)
  (cond ((< x 0.0)
         0.0)
        ((>= x 1.0)
         1.0)
        (else
         (beta-inc-axpy 1.0 0.0 a b x))))