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1 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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3 ;;
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4 ;; Monte-Carlo application examples
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5 ;;
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6 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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8
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9 (ns
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10 #^{:author "Konrad Hinsen"
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11 :skip-wiki true
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12 :doc "Examples for monte carlo methods"}
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13 clojure.contrib.probabilities.random.examples-monte-carlo
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14 (:require [clojure.contrib.generic.collection :as gc])
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15 (:use [clojure.contrib.probabilities.random-numbers
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16 :only (lcg rand-stream)])
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17 (:use [clojure.contrib.probabilities.finite-distributions
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18 :only (uniform)])
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19 (:use [clojure.contrib.probabilities.monte-carlo
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20 :only (random-stream discrete interval normal lognormal exponential
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21 n-sphere
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22 sample sample-sum sample-mean sample-mean-variance)]
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23 :reload)
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24 (:use [clojure.contrib.monads
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25 :only (domonad state-m)]))
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26
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27 ; Create a linear congruential generator
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28 (def urng (lcg 259200 7141 54773 1))
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29
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30 ;; Use Clojure's built-in random number generator
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31 ;(def urng rand-stream)
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32
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33 ; Sample transformed distributions
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34 (defn sample-distribution
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35 [n rt]
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36 (take n (gc/seq (random-stream rt urng))))
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37
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38 ; Interval [-2, 2)
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39 (sample-distribution 10 (interval -2 2))
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40 ; Compare with a direct transformation
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41 (= (sample-distribution 10 (interval -2 2))
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42 (map (fn [x] (- (* 4 x) 2)) (take 10 (gc/seq urng))))
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43
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44 ; Normal distribution
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45 (sample-distribution 10 (normal 0 1))
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46
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47 ; Log-Normal distribution
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48 (sample-distribution 10 (lognormal 0 1))
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49
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50 ; Exponential distribution
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51 (sample-distribution 10 (exponential 1))
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52
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53 ; n-sphere distribution
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54 (sample-distribution 10 (n-sphere 2 1))
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55
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56 ; Discrete distribution
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57 (sample-distribution 10 (discrete (uniform (range 1 7))))
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58
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59 ; Compose distributions in the state monad
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60 (def sum-two-dists
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61 (domonad state-m
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62 [r1 (interval -2 2)
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63 r2 (normal 0 1)]
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64 (+ r1 r2)))
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65
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66 (sample-distribution 10 sum-two-dists)
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67
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68 ; Distribution transformations
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69 (sample-distribution 5 (sample 2 (interval -2 2)))
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70 (sample-distribution 10 (sample-sum 10 (interval -2 2)))
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71 (sample-distribution 10 (sample-mean 10 (interval -2 2)))
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72 (sample-distribution 10 (sample-mean-variance 10 (interval -2 2)))
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73
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