#lang scheme/base
;;; PLT Scheme Science Collection
;;; random-distributions/bernoulli.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 module implements the bernoulli 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)
;;; 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 required for V4.0.  (Doug Williams)

(require (lib "contract.ss"))

(provide
 (rename-out (random-binomial unchecked-random-binomial)
             (binomial-pdf unchecked-binomial-pdf)))

(provide/contract
 (random-binomial
  (case-> (-> random-source? (real-in 0.0 1.0) natural-number/c natural-number/c)
          (-> (real-in 0.0 1.0) natural-number/c natural-number/c)))
 (binomial-pdf
  (-> natural-number/c (real-in 0.0 1.0) natural-number/c (>=/c 0.0))))

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

;;; random-binomial: random-source x real x integer -> integer
;;; random-binomial: real x integer -> integer
;;; This routine returns a random variate from a binomial distribution
;;; with n independent trials and probability p.
(define random-binomial
  (case-lambda
    ((r p n)
     (let ((a 0)
           (b 0)
           (k 0))
       (let loop ()
         (when (> n 10)
           (begin
             (set! a (+ 1 (quotient n 2)))
             (set! b (+ 1 n (- a)))
             (let ((x (unchecked-random-beta 
                       r
                       (exact->inexact a)
                       (exact->inexact b))))
               (if (>= x p)
                   (begin
                     (set! n (- a 1))
                     (set! p (/ p x)))
                   (begin
                     (set! k (+ k a))
                     (set! n (- b 1))
                     (set! p (/ (- p x) (- 1.0 x))))))
             (loop))))
       (do ((i 0 (+ i 1)))
           ((= i n) k)
         (let ((u (unchecked-random-uniform r)))
           (when (< u p)
             (set! k (+ k 1)))))))
    ((p n)
     (random-binomial (current-random-source) p n))))

;;; binomial-pdf: integer x real x integer -> real
;;; This function computes the probability density p(x) at x for a
;;; binomial distribution with n independent trials and probability p.
(define (binomial-pdf k p n)
  (if (> k n)
      0.0
      (let ((ln_c_nk (unchecked-lnchoose n k)))
        (exp (+ ln_c_nk
                (* k (log p))
                (* (- n k)
                   (log (- 1.0 p))))))))