measurable

commit 952dc91af3fa62c50b9d3ca1379d5b3727c0e2f5
parent 35b056093e0b817dd0a7240416ce07b51287f5e1
Author: Jared Tobin <jared@jtobin.ca>
Date:   Sat, 19 Oct 2013 21:15:13 +1300

Add 'to', 'cdf'.

Diffstat:
M
src/Measurable.hs
 | 
29
+++++++++++++++++++++++++++++
M
tests/Test.hs
 | 
20
+++++++++++++++++---

2 files changed, 46 insertions(+), 3 deletions(-)
diff --git a/src/Measurable.hs b/src/Measurable.hs
@@ -110,3 +110,32 @@ weightedAverage :: Fractional c => (a -> c) -> [a] -> c
 weightedAverage f = average . map f
 {-# INLINE weightedAverage #-}
 
+-- | Integrate from a to b.
+to :: (Num a, Ord a) => a -> a -> a -> a
+to a b x | x >= a && x <= b = 1
+         | otherwise        = 0
+
+-- | Cumulative distribution function for a measure.
+--
+--   Really cool; works perfectly in both discrete and continuous cases.
+--
+--   > let f = cdf (fromObservations [1..10])
+--   > cdf 0
+--   0.0
+--   > cdf 1
+--   0.1
+--   > cdf 10
+--   1.0
+--   > cdf 11
+--   1.0
+--
+--   > let g = cdf (fromDensity standardNormal)
+--   > cdf 0
+--   0.504
+--   > cdf 1
+--   0.838
+--   > cdf (1 / 0)
+--   0.999
+cdf :: Measure Double -> Double -> Double
+cdf mu b = mean $ negate (1 / 0) `to` b <$> mu
+
diff --git a/tests/Test.hs b/tests/Test.hs
@@ -1,6 +1,8 @@
 -- Simple examples that demonstrate some measure-foo.
 
+import Control.Applicative
 import Control.Monad
+import Control.Monad.Trans
 import Measurable
 import Statistics.Distribution hiding (mean, variance)
 import Statistics.Distribution.Normal
@@ -20,8 +22,8 @@ main = do
 
   let mu  = fromDensity standardNormal
       nu  = fromObservations expSamples
-      rho = (fmap cos mu) + (fmap sin nu)
-      eta = fmap exp rho
+      rho = (cos <$> mu) + (sin <$> nu)
+      eta = exp <$> rho
 
   putStrLn $ "mean of normal samples (should be around 0):                " ++ 
                show (mean . fromObservations $ normSamples)
@@ -55,7 +57,19 @@ main = do
                show (variance zeta)
 
   let alpha = fromDensity $ density $ chiSquared 5
+      beta  = (exp . tanh) <$> (phi * alpha)
 
   putStrLn $ "let X ~ N(2, 1), Y ~ chisq(5).  variance of exp (tanh XY)   " ++
-               show (variance . fmap (exp . tanh) $ phi * alpha)
+               show (variance beta)
+
+  putStrLn ""
+  putStrLn "Some probability examples:"
+  putStrLn ""
+
+  putStrLn $ "let X ~ N(0, 1).  P(X < 0) (should be ~ 0.5):               " ++
+               show (mean $ negate (1 / 0) `to` 0 <$> mu)
+
+  putStrLn $ "let X ~ N(0, 1).  P(0 < X < 1) (should be ~ 0.341):         " ++
+               show (mean $ 0 `to` 1 <$> mu)
+