Stability | experimental |
---|---|

Maintainer | Alexey Khudyakov <alexey.skladnoy@gmail.com> |

- class Monoid m => StatMonoid m a where
- pappend :: a -> m -> m

- evalStatistic :: (Foldable d, StatMonoid m a) => d a -> m
- data TwoStats a b = TwoStats {}

# Type class

class Monoid m => StatMonoid m a whereSource

Monoid which corresponds to some stattics. In order to do so it
must be commutative. In many cases it's not practical to
construct monoids for each element so `papennd`

was added.
First parameter of type class is monoidal accumulator. Second is
type of element over which statistic is calculated.

Statistic could be calculated with fold over sample. Since
accumulator is `Monoid`

such fold could be easily parralelized.
Check examples section for more information.

Instance must satisfy following law:

pappend x (pappend y mempty) == pappend x mempty `mappend` pappend y mempty mappend x y == mappend y x

It is very similar to Reducer type class from monoids package but require commutative monoids

Add one element to monoid accumulator. P stands for point in analogy for Pointed.

StatMonoid Max Double | |

StatMonoid Min Double | |

Real a => StatMonoid Variance a | |

Real a => StatMonoid Mean a | |

Integral a => StatMonoid (Count a) b | |

(StatMonoid a x, StatMonoid b x) => StatMonoid (TwoStats a b) x |

evalStatistic :: (Foldable d, StatMonoid m a) => d a -> mSource

Calculate statistic over `Foldable`

. It's implemented in terms of
foldl'.

## Examples

These examples show how to find maximum and minimum of a sample in one pass over data.

This is test data. It's not limited to list but could be anything what could be folded.

> let xs = [1..100] :: [Double]

Now let calculate maximum of test sample using two methods. First
one is to use generic function `evalStatistic`

and another one is
fold.

> evalStatistic xs :: Max Max {calcMax = 100.0} > foldl (flip pappend) mempty xs :: Max Max {calcMax = 100.0}

More complicated example allows to combine several monoids together. It allows to calculate two statistics in one pass:

> evalStatistic xs :: TwoStats Min Max TwoStats {calcStat1 = Min {calcMin = 1.0}, calcStat2 = Max {calcMax = 100.0}}

Last example shows how to calculate nuber of elements, mean and variance at once:

> let v = evalStatistic xs :: Variance > calcCount v 100 > calcMean v 50.5 > calcStddev v 28.86607004772212

Monoid which allows to calculate two statistics in parralel

# Additional information

Statistic is function of a sample which does not depend on order of elements in a sample. For each statistics corresponding monoid could be constructed:

f :: [A] -> B data F = F [A] evalF (F xs) = f xs instance Monoid F here mempty = F [] (F a) `mappend` (F b) = F (a ++ b)

This indeed proves that monoid could be constructed. Monoid above is completely impractical. It runs in O(n) space. However for some statistics monoids which runs in O(1) space could be implemented. Simple examples of such statistics are number of elements in sample or mean of a sample.

On the other hand some statistics could not be implemented in such way. For example calculation of median require O(n) space. Variance could be implemented in O(1) but such implementation will have problems with numberical stability.