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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;;
;; Monte-Carlo application examples
;;
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(ns
#^{:author "Konrad Hinsen"
:skip-wiki true
:doc "Examples for monte carlo methods"}
clojure.contrib.probabilities.random.examples-monte-carlo
(:require [clojure.contrib.generic.collection :as gc])
(:use [clojure.contrib.probabilities.random-numbers
:only (lcg rand-stream)])
(:use [clojure.contrib.probabilities.finite-distributions
:only (uniform)])
(:use [clojure.contrib.probabilities.monte-carlo
:only (random-stream discrete interval normal lognormal exponential
n-sphere
sample sample-sum sample-mean sample-mean-variance)]
:reload)
(:use [clojure.contrib.monads
:only (domonad state-m)]))
; Create a linear congruential generator
(def urng (lcg 259200 7141 54773 1))
;; Use Clojure's built-in random number generator
;(def urng rand-stream)
; Sample transformed distributions
(defn sample-distribution
[n rt]
(take n (gc/seq (random-stream rt urng))))
; Interval [-2, 2)
(sample-distribution 10 (interval -2 2))
; Compare with a direct transformation
(= (sample-distribution 10 (interval -2 2))
(map (fn [x] (- (* 4 x) 2)) (take 10 (gc/seq urng))))
; Normal distribution
(sample-distribution 10 (normal 0 1))
; Log-Normal distribution
(sample-distribution 10 (lognormal 0 1))
; Exponential distribution
(sample-distribution 10 (exponential 1))
; n-sphere distribution
(sample-distribution 10 (n-sphere 2 1))
; Discrete distribution
(sample-distribution 10 (discrete (uniform (range 1 7))))
; Compose distributions in the state monad
(def sum-two-dists
(domonad state-m
[r1 (interval -2 2)
r2 (normal 0 1)]
(+ r1 r2)))
(sample-distribution 10 sum-two-dists)
; Distribution transformations
(sample-distribution 5 (sample 2 (interval -2 2)))
(sample-distribution 10 (sample-sum 10 (interval -2 2)))
(sample-distribution 10 (sample-mean 10 (interval -2 2)))
(sample-distribution 10 (sample-mean-variance 10 (interval -2 2)))
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