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     3 ;;

     4 ;; Monte-Carlo application examples

     5 ;;

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     8 

     9 (ns

    10   #^{:author "Konrad Hinsen"

    11      :skip-wiki true

    12      :doc "Examples for monte carlo methods"}

    13   clojure.contrib.probabilities.random.examples-monte-carlo

    14   (:require [clojure.contrib.generic.collection :as gc])

    15   (:use [clojure.contrib.probabilities.random-numbers

    16 	 :only (lcg rand-stream)])

    17   (:use [clojure.contrib.probabilities.finite-distributions

    18 	 :only (uniform)])

    19   (:use [clojure.contrib.probabilities.monte-carlo

    20 	 :only (random-stream discrete interval normal lognormal exponential

    21 		n-sphere

    22 		sample sample-sum sample-mean sample-mean-variance)]

    23 	:reload)

    24   (:use [clojure.contrib.monads

    25 	:only (domonad state-m)]))

    26 

    27 ; Create a linear congruential generator

    28 (def urng (lcg 259200 7141 54773 1))

    29 

    30 ;; Use Clojure's built-in random number generator

    31 ;(def urng rand-stream)

    32 

    33 ; Sample transformed distributions

    34 (defn sample-distribution

    35   [n rt]

    36   (take n (gc/seq (random-stream rt urng))))

    37 

    38 ; Interval [-2, 2)

    39 (sample-distribution 10 (interval -2 2))

    40 ; Compare with a direct transformation

    41 (= (sample-distribution 10 (interval -2 2))

    42    (map (fn [x] (- (* 4 x) 2)) (take 10 (gc/seq urng))))

    43 

    44 ; Normal distribution

    45 (sample-distribution 10 (normal 0 1))

    46 

    47 ; Log-Normal distribution

    48 (sample-distribution 10 (lognormal 0 1))

    49 

    50 ; Exponential distribution

    51 (sample-distribution 10 (exponential 1))

    52 

    53 ; n-sphere distribution

    54 (sample-distribution 10 (n-sphere 2 1))

    55 

    56 ; Discrete distribution

    57 (sample-distribution 10 (discrete (uniform (range 1 7))))

    58 

    59 ; Compose distributions in the state monad

    60 (def sum-two-dists

    61   (domonad state-m

    62     [r1 (interval -2 2)

    63      r2 (normal 0 1)]

    64     (+ r1 r2)))

    65 

    66 (sample-distribution 10 sum-two-dists)

    67 

    68 ; Distribution transformations

    69 (sample-distribution  5 (sample 2 (interval -2 2)))

    70 (sample-distribution 10 (sample-sum 10 (interval -2 2)))

    71 (sample-distribution 10 (sample-mean 10 (interval -2 2)))

    72 (sample-distribution 10 (sample-mean-variance 10 (interval -2 2)))

    73
author	Robert McIntyre <rlm@mit.edu>
date	Sat, 21 Aug 2010 06:25:44 -0400
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