[Haskell-cafe] Re: Math.Statistics

[ChrisK]

ok wrote:
> There are a number of interesting issues raised by mbeddoe's
> Math.Statistics.
> 
>     data (Floating a, Ord a)
>       => Simple_Continuous_Variate a
>        = SCV [a] Int a a (Array Int a)
> 
>     list_to_variate xs = SCV xs n m s o
>       where n = length xs
>             m = sum xs / fromIntegral n
>             s = sum [(x - m)^2 | x <- xs] / fromIntegral (n - 1)
>             o = listArray (1,n) (sort xs)
> 
>     vLength (SCV _ n _ _ _) = n
>     vMean   (SCV _ _ m _ _) = m
>     vSd     (SCV _ _ _ s _) = s
>     vMin    (SCV _ _ _ _ a) = a ! 1
>     vMax    (SCV _ n _ _ a) = a ! n
>     vRange   scv            = vMax scv - vMin scv
>     vMedian (SCV _ n _ _ a)
>       | odd n               = a ! ((n+1)`div`2)
>       | even n              = ((a ! l) + (a ! u))/2
>                               where l = n `div` 2
>                                     u = n - l
>     .....

Math.Statistics eats many good names. I would also suggest offering a type class
interface.  Then you could operate on various containers besides a list:

-- A class for extracting a summary number from a type.
-- None of these make much sense without Ord.
-- I could imagine using (+) and `div` so why require (/)?
class (Ord b) => SingleStat a b | a -> b where
   samples :: a -> Integer  -- lump in with SingleStat
   mean :: a -> b
   var :: a -> b
   stddev :: a -> b
   moment :: Int -> a -> b
   range :: a -> b
   min :: a -> b
   max :: a -> b
   median :: a -> b

instance SingleStat [Integer] Integer where ...
instance SingleStat [Double] Double where ...
instance (Ix i) => SingleStat (Array i Double) Double where ...
instance SingleStat (Simple_Continuous_Variate a) where ...

-- And then I could make interesting things like Histogram,
-- where the data is Int's but the statistics are Doubles:

newtype Histogram = Histogram (Map Int Int)
instance SingleStat Histogram Double where ...

Cheers,
  Chris