;;; PLT Scheme Science Collection
;;; random-distributions/pareto.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 pareto 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 pareto mzscheme
  
  (require (lib "contract.ss"))
  
  (provide/contract
   (random-pareto
    (case-> (-> random-source? real? real? real?)
            (-> real? real? real?)))
   (pareto-pdf
    (-> real? real? real? (>=/c 0.0)))
   (pareto-cdf
    (-> real? real? real? (real-in 0.0 1.0))))
  
  (require "../random-source.ss")
  
  ;; random-pareto: ransom-source x real x real -> real
  ;; random-pareto: real x real -> real
  ;; This function returns a random variate from the Pareto
  ;; distribution of order a.  The distribution funtion is
  ;;   p(x) dx = (a/b) / (x/b)^(a+1) dx
  (define random-pareto
    (case-lambda
      ((r a b)
       (let* ((x (random-uniform r))
              (z (expt x (/ -1.0 a))))
         (* b z)))
      ((a b)
       (random-pareto (current-random-source) a b))))
  
  ;; pareto-pdf: real x real x real -> real
  ;; This function computes the probability density function p(x) at x
  ;; for a Pareto distribution with exponent a and scale b using the
  ;; formula above.
  (define (pareto-pdf x a b)
    (if (>= x b)
        (/ (/ a b) (expt (/ x b) (+ a 1.0)))
        0.0))
  
  ;; pareto-cdf: real x real x real -> real
  ;; This function computes the cumulative density function D(x) for
  ;; the Pareto distribution with exponent a and scale b.
  (define (pareto-cdf x a b)
    (if (< x b)
        0.0
        (- 1.0 (expt (/ b x) a))))
  
)