measurable

commit caf2c4a3db97c660c99cf29b088fe171a7c5b88a
parent 80164e3efa5ed478ac8c8f548722d5651cf6f8a1
Author: Jared Tobin <jared@jtobin.ca>
Date:   Sat, 19 Oct 2013 16:34:58 +1300

Update examples.  Kind of mind-blowing.

Diffstat:
M
src/Measurable.hs
 | 
20
+++++++++++++-------
M
tests/Test.hs
 | 
26
+++++++++++++++++++++++++-

2 files changed, 38 insertions(+), 8 deletions(-)
diff --git a/src/Measurable.hs b/src/Measurable.hs
@@ -71,7 +71,8 @@ push :: (a -> b) -> Measure a -> Measure b
 push f mu = Measure pushforward
   where pushforward g = measure mu $ g . f
 
--- | The volume is obtained by integrating against a constant.
+-- | The volume is obtained by integrating against a constant.  This is '1' for
+--   any probability measure.
 volume :: Measure a -> Double
 volume mu = measure mu (const 1)
 
@@ -99,16 +100,21 @@ convolute mu nu = Measure $ \f -> measure nu
                             $ \y -> measure mu
                               $ \x -> f (x + y)
 
+-- | Measure subtraction. (does this make sense?)
+msubtract mu nu = Measure $ \f -> measure nu
+                            $ \y -> measure mu
+                              $ \x -> f (x - y)
+
+-- | Measure multiplication. (does this make sense?)
+prod :: Num a => Measure a -> Measure a -> Measure a
+prod mu nu = Measure $ \f -> measure nu
+                       $ \y -> measure mu
+                         $ \x -> f (x * y)
+
 -- | The (sum) identity measure.
 identityMeasure :: Fractional a => Measure a
 identityMeasure = fromObservations []
 
--- | Lebesgue measure.
-lebesgue :: Double -> Double -> Measure Double
-lebesgue a b = fromDensity rectangle
-  where rectangle x | x >= a && x <= b = 1
-                    | otherwise        = 0
- 
 -- | Simple average.
 average :: Fractional a => [a] -> a
 average xs = fst $ foldl' 
diff --git a/tests/Test.hs b/tests/Test.hs
@@ -13,10 +13,12 @@ import Control.Monad
 import Measurable
 import Statistics.Distribution hiding (mean, variance)
 import Statistics.Distribution.Normal
+import Statistics.Distribution.ChiSquared
 import System.Random.MWC
 import System.Random.MWC.Distributions
 
-standardNormal = density $ normalDistr 0 1
+standardNormal      = density $ normalDistr 0 1
+genLocationNormal m = density $ normalDistr m 1
 
 main = do
   expSamples <- withSystemRandom . asGenIO $ \g -> 
@@ -37,3 +39,25 @@ main = do
   putStrLn $ "let X ~ N(0, 1), Y ~ observed.  mean of exp(cos X + sin Y): " ++
                show (mean eta)
 
+  putStrLn ""
+  putStrLn "and now some 'woah, this actally seems to make sense' examples:"
+  putStrLn ""
+
+  let iota = mu `msubtract` mu
+  
+  putStrLn $ "let X, Y be independent N(0, 1).  mean of X - Y:            " ++
+               show (mean iota)
+  putStrLn $ "let X, Y be independent N(0, 1).  variance of X - Y:        " ++
+               show (variance iota)
+
+  -- 
+
+  let phi  = fromDensity $ genLocationNormal 2
+      xi   = fromDensity $ genLocationNormal 3
+      zeta = prod phi xi
+
+  putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). mean of XY (should be 6)      " ++
+               show (mean zeta)
+  putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). variance of XY (should be 14) " ++
+               show (variance zeta)
+