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+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;
+;; Monte-Carlo application examples
+;;
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+
+(ns 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)))
+