```{-# LANGUAGE FlexibleContexts #-}
-- | Pearson's chi squared test.
module Statistics.Test.ChiSquared (
chi2test
, chi2testCont
, module Statistics.Test.Types
) where

import Prelude hiding (sum)

import Statistics.Distribution
import Statistics.Distribution.ChiSquared
import Statistics.Function        (square)
import Statistics.Sample.Internal (sum)
import Statistics.Test.Types
import Statistics.Types
import qualified Data.Vector as V
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as U

-- | Generic form of Pearson chi squared tests for binned data. Data
--   sample is supplied in form of tuples (observed quantity,
--   expected number of events). Both must be positive.
--
--   This test should be used only if all bins have expected values of
--   at least 5.
chi2test :: (G.Vector v (Int,Double), G.Vector v Double)
=> Int                 -- ^ Number of additional degrees of
--   freedom. One degree of freedom
--   is due to the fact that the are
--   N observation in total and
--   accounted for automatically.
-> v (Int,Double)      -- ^ Observation and expectation.
-> Maybe (Test ChiSquared)
chi2test ndf vec
| ndf <  0  = error \$ "Statistics.Test.ChiSquare.chi2test: negative NDF " ++ show ndf
| n   > 0   = Just Test
{ testSignificance = mkPValue \$ complCumulative d chi2
, testStatistics   = chi2
, testDistribution = chiSquared ndf
}
| otherwise = Nothing
where
n     = G.length vec - ndf - 1
chi2  = sum \$ G.map (\(o,e) -> square (fromIntegral o - e) / e) vec
d     = chiSquared n
{-# INLINABLE  chi2test #-}
{-# SPECIALIZE
chi2test :: Int -> U.Vector (Int,Double) -> Maybe (Test ChiSquared) #-}
{-# SPECIALIZE
chi2test :: Int -> V.Vector (Int,Double) -> Maybe (Test ChiSquared) #-}

-- | Chi squared test for data with normal errors. Data is supplied in
--   form of pair (observation with error, and expectation).
chi2testCont
:: (G.Vector v (Estimate NormalErr Double, Double), G.Vector v Double)
=> Int                                   -- ^ Number of additional
--   degrees of freedom.
-> v (Estimate NormalErr Double, Double) -- ^ Observation and expectation.
-> Maybe (Test ChiSquared)
chi2testCont ndf vec
| ndf < 0   = error \$ "Statistics.Test.ChiSquare.chi2testCont: negative NDF " ++ show ndf
| n   > 0   = Just Test
{ testSignificance = mkPValue \$ complCumulative d chi2
, testStatistics   = chi2
, testDistribution = chiSquared ndf
}
| otherwise = Nothing
where
n     = G.length vec - ndf - 1
chi2  = sum \$ G.map (\(Estimate o (NormalErr s),e) -> square (o - e) / s) vec
d     = chiSquared n
```