measurable

commit beeb0d0bb77da493152e18f8c1e500b61d186ad5
parent 952dc91af3fa62c50b9d3ca1379d5b3727c0e2f5
Author: Jared Tobin <jared@jtobin.ca>
Date:   Sat, 19 Oct 2013 21:35:52 +1300

Change 'mean' to 'expectation' everywhere.

Diffstat:
M
src/Measurable.hs
 | 
12
++++++------
M
tests/Test.hs
 | 
15
+++++++++------

2 files changed, 15 insertions(+), 12 deletions(-)
diff --git a/src/Measurable.hs b/src/Measurable.hs
@@ -78,13 +78,13 @@ instance Monad Measure where
 volume :: Measure a -> Double
 volume mu = measure mu (const 1)
 
--- | The mean is obtained by integrating against the identity function.
-mean :: Measure Double -> Double
-mean mu = measure mu id
+-- | The expectation is obtained by integrating against the identity function.
+expectation :: Measure Double -> Double
+expectation mu = measure mu id
 
 -- | The variance is obtained by integrating against the usual function.
 variance :: Measure Double -> Double
-variance mu = measure mu (^ 2) - mean mu ^ 2
+variance mu = measure mu (^ 2) - expectation mu ^ 2
 
 -- | Create a measure from a collection of observations from some distribution.
 fromObservations :: Fractional a => [a] -> Measure a
@@ -103,7 +103,7 @@ identityMeasure = fromObservations []
 average :: Fractional a => [a] -> a
 average xs = fst $ foldl' 
   (\(!m, !n) x -> (m + (x - m) / fromIntegral (n + 1), n + 1)) (0, 0) xs
-{-# INLINE mean #-}
+{-# INLINE average #-}
 
 -- | Weighted average.
 weightedAverage :: Fractional c => (a -> c) -> [a] -> c
@@ -137,5 +137,5 @@ to a b x | x >= a && x <= b = 1
 --   > cdf (1 / 0)
 --   0.999
 cdf :: Measure Double -> Double -> Double
-cdf mu b = mean $ negate (1 / 0) `to` b <$> mu
+cdf mu b = expectation $ negate (1 / 0) `to` b <$> mu
 
diff --git a/tests/Test.hs b/tests/Test.hs
@@ -26,11 +26,11 @@ main = do
       eta = exp <$> rho
 
   putStrLn $ "mean of normal samples (should be around 0):                " ++ 
-               show (mean . fromObservations $ normSamples)
+               show (expectation . fromObservations $ normSamples)
   putStrLn $ "variance of normal samples (should be around 1):            " ++ 
                show (variance . fromObservations $ normSamples)
   putStrLn $ "let X ~ N(0, 1), Y ~ observed.  mean of exp(cos X + sin Y): " ++
-               show (mean eta)
+               show (expectation eta)
 
   putStrLn ""
   putStrLn "and now some 'woah, this actally seems to make sense' examples:"
@@ -41,7 +41,7 @@ main = do
   let iota = mu - mu
   
   putStrLn $ "let X, Y be independent N(0, 1).  mean of X - Y:            " ++
-               show (mean iota)
+               show (expectation iota)
   putStrLn $ "let X, Y be independent N(0, 1).  variance of X - Y:        " ++
                show (variance iota)
 
@@ -52,7 +52,7 @@ main = do
       zeta = phi * xi
 
   putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). mean of XY (should be 6)      " ++
-               show (mean zeta)
+               show (expectation zeta)
   putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). variance of XY (should be 14) " ++
                show (variance zeta)
 
@@ -67,9 +67,12 @@ main = do
   putStrLn ""
 
   putStrLn $ "let X ~ N(0, 1).  P(X < 0) (should be ~ 0.5):               " ++
-               show (mean $ negate (1 / 0) `to` 0 <$> mu)
+               show (cdf mu 0)
 
   putStrLn $ "let X ~ N(0, 1).  P(0 < X < 1) (should be ~ 0.341):         " ++
-               show (mean $ 0 `to` 1 <$> mu)
+               show (expectation $ 0 `to` 1 <$> mu)
+
+  putStrLn $ "let X ~ N(0, 1), Y ~ observed.  P(0 < X < 0.8):             " ++
+               show (expectation $ 0 `to` 0.8 <$> (mu + nu))