|Maintainer||Alexey Khudyakov <email@example.com>|
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
Monoid such fold could be easily parralelized.
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.
Calculate statistic over
Foldable. It's implemented in terms of
Monoid which allows to calculate two statistics in parralel
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. For example mean.
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 won't be numerically stable.