root/trunk/random/exponential.lisp

;; Exponential distribution
;; Liam Healy, Sat Sep  2 2006 - 19:04
;; Time-stamp: <2008-02-17 12:34:11EST exponential.lisp>
;; $Id$

(in-package :gsl)

(defmfun exponential (generator mu)
  "gsl_ran_exponential"
  (((generator generator) :pointer) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "A random variate from the exponential distribution
   with mean mu. The distribution is
   p(x) dx = {1 \over \mu} \exp(-x/\mu) dx
   x >= 0.")

(defmfun exponential-pdf (x mu)
  "gsl_ran_exponential_pdf" ((x :double) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "The probability density p(x) at x
  for an exponential distribution with mean mu, using the formula
  given for exponential.")

(defmfun exponential-P (x mu)
  "gsl_cdf_exponential_P" ((x :double) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "The cumulative distribution function
   P(x) for the exponential distribution with mean mu.")

(defmfun exponential-Q (x mu)
  "gsl_cdf_exponential_Q" ((x :double) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "The cumulative distribution function
   Q(x) for the exponential distribution with mean mu.")

(defmfun exponential-Pinv (P mu)
  "gsl_cdf_exponential_Pinv" ((P :double) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "The inverse cumulative distribution function
   P(x) for the exponential distribution with mean mu.")

(defmfun exponential-Qinv (Q mu)
  "gsl_cdf_exponential_Qinv" ((Q :double) (mu :double))
  :c-return :double
  :documentation                        ; FDL
  "The inverse cumulative distribution function
   Q(x) for the exponential distribution with mean mu.")

;;; Examples and unit test
#|
(make-tests exponential
  (letm ((rng (random-number-generator *mt19937* 0)))
      (loop for i from 0 to 10
            collect
            (exponential rng 10.0d0)))
  (exponential-pdf 0.0d0 10.0d0)
  (exponential-p 1.0d0 2.0d0)
  (exponential-q 1.0d0 2.0d0)
  (exponential-pinv 0.3934693402873666d0 2.0d0)
  (exponential-qinv 0.6065306597126334d0 2.0d0))
|#

(LISP-UNIT:DEFINE-TEST EXPONENTIAL
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST
    (LIST 0.0025828444588394794d0 18.145581427987647d0
          12.636598054339759d0 0.5424387252062355d0
          14.624994234158105d0 7.236607929535993d0
          0.4345362449683603d0 2.95303920904529d0
          6.161052939065796d0 3.011686333539114d0
          2.7451079819355364d0))
   (MULTIPLE-VALUE-LIST
    (LETM ((RNG (RANDOM-NUMBER-GENERATOR *MT19937* 0)))
      (LOOP FOR I FROM 0 TO 10 COLLECT
            (EXPONENTIAL RNG 10.0d0)))))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL (LIST 0.1d0)
                                     (MULTIPLE-VALUE-LIST
                                      (EXPONENTIAL-PDF
                                       0.0d0 10.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.3934693402873666d0)
   (MULTIPLE-VALUE-LIST (EXPONENTIAL-P 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.6065306597126334d0)
   (MULTIPLE-VALUE-LIST (EXPONENTIAL-Q 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL (LIST 1.0d0)
                                     (MULTIPLE-VALUE-LIST
                                      (EXPONENTIAL-PINV
                                       0.3934693402873666d0
                                       2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL (LIST 1.0d0)
                                     (MULTIPLE-VALUE-LIST
                                      (EXPONENTIAL-QINV
                                       0.6065306597126334d0
                                       2.0d0))))