root/trunk/random/gumbel2.lisp

;; The Gumbel type 2 random number distribution
;; Liam Healy, Sun Oct 29 2006
;; Time-stamp: <2008-02-17 13:32:16EST gumbel2.lisp>
;; $Id$

(in-package :gsl)

(defmfun gumbel2 (generator a b)
  "gsl_ran_gumbel2"
  (((generator generator) :pointer) (a :double) (b :double))
  :c-return :double
  :documentation                        ; FDL
  "A random variate from the Type-2 Gumbel
   distribution, p(x) dx = a b x^{-a-1} \exp(-b x^{-a}) dx
   for 0 < x < \infty.")

(defmfun gumbel2-pdf (x a b)
  "gsl_ran_gumbel2_pdf" ((x :double) (a :double) (b :double))
  :c-return :double
  :documentation                        ; FDL
  "The probability density p(x) at x
   for a Type-2 Gumbel distribution with parameters a and b,
   using the formula given in #'gumbel2.")

(defmfun gumbel2-P (x a b)
  "gsl_cdf_gumbel2_P" ((x :double) (a :double) (b :double))
  :c-return :double                     ; FDL
  :documentation "The cumulative distribution functions
  P(x) for the Type-2 Gumbel distribution with
  parameters a and b.")

(defmfun gumbel2-Q (x a b)
  "gsl_cdf_gumbel2_Q" ((x :double) (a :double) (b :double))
  :c-return :double
  :documentation                        ; FDL
  "The cumulative distribution functions
  Q(x) for the Type-2 Gumbel distribution with
  parameters a and b.")

(defmfun gumbel2-Pinv (P a b)
  "gsl_cdf_gumbel2_Pinv" ((P :double) (a :double) (b :double))
  :c-return :double
  :documentation                        ; FDL
  "The inverse cumulative distribution functions
  P(x) for the Type-2 Gumbel distribution with
  parameters a and b.")

(defmfun gumbel2-Qinv (Q a b)
  "gsl_cdf_gumbel2_Qinv" ((Q :double) (a :double) (b :double))
  :c-return :double
  :documentation                        ; FDL
  "The inverse cumulative distribution functions
  Q(x) for the Type-2 Gumbel distribution with
  parameters a and b.")

;;; Examples and unit test
#|
(make-tests gumbel2
  (letm ((rng (random-number-generator *mt19937* 0)))
      (loop for i from 0 to 10
            collect
            (gumbel2 rng 1.0d0 2.0d0)))
  (gumbel2-pdf 5.0d0 1.0d0 2.0d0)
  (gumbel2-P 10.0d0 1.0d0 2.0d0)
  (gumbel2-Q 10.0d0 1.0d0 2.0d0)
  (gumbel2-Pinv 0.8187307530779818d0 1.0d0 2.0d0)
  (gumbel2-Qinv 0.18126924692201815d0 1.0d0 2.0d0))
|#

(LISP-UNIT:DEFINE-TEST GUMBEL2
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST
    (LIST 7743.400858519516d0 1.102196701680339d0
          1.5827044520998628d0 36.87052393317972d0
          1.3675219066608615d0 2.7637257945633085d0
          46.026080060263446d0 6.772683525074477d0
          3.2461983686562204d0 6.640797807286079d0
          7.285687897019733d0))
   (MULTIPLE-VALUE-LIST
    (LETM ((RNG (RANDOM-NUMBER-GENERATOR *MT19937* 0)))
      (LOOP FOR I FROM 0 TO 10 COLLECT
            (GUMBEL2 RNG 1.0d0 2.0d0)))))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.053625603682851145d0)
   (MULTIPLE-VALUE-LIST (GUMBEL2-PDF 5.0d0 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.8187307530779818d0)
   (MULTIPLE-VALUE-LIST (GUMBEL2-P 10.0d0 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.18126924692201815d0)
   (MULTIPLE-VALUE-LIST (GUMBEL2-Q 10.0d0 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 9.999999999999998d0)
   (MULTIPLE-VALUE-LIST
    (GUMBEL2-PINV 0.8187307530779818d0 1.0d0 2.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 10.0d0)
   (MULTIPLE-VALUE-LIST (GUMBEL2-QINV 0.18126924692201815d0 1.0d0 2.0d0))))