Safe Haskell | Safe-Inferred |
---|---|

Language | Haskell2010 |

This module provides incremental statistics folds based upon the foldl library

To avoid clashes, Control.Foldl should be qualified.

`>>>`

`import Control.Foldl.Incremental`

`>>>`

`import qualified Control.Foldl as L`

The folds represent incremental statistics such as `moving averages`.

Statistics are based on exponential-weighting schemes which enable statistics to be calculated in a streaming one-pass manner. The stream of moving averages with a `rate`

of 0.9 is:

`>>>`

`L.scan (incMa 0.9) [1..10]`

or if you just want the moving average at the end.

`>>>`

`L.fold (incMa 0.9) [1..10]`

# Increment

An Increment is the incremental state within an exponential moving average fold.

incrementalize :: (a -> Double) -> Double -> Fold a Double Source

Incrementalize takes a function and turns it into a `Fold`

where the step incremental is an Increment with a step function iso to a step in an exponential moving average calculation.

`>>>`

`incrementalize id`

is a moving average of a foldable

`>>>`

`incrementalize (*2)`

is a moving average of the square of a foldable

This lets you build an exponential standard deviation computation (using Foldl) as

`>>>`

`std r = (\s ss -> sqrt (ss - s**2)) <$> incrementalize id r <*> incrementalize (*2) r`

An exponential moving average approach (where `average`

id abstracted to `function`

) represents an efficient single-pass computation that attempts to keep track of a running average of some Foldable.

The rate is the parameter regulating the discount of current state and the introduction of the current value.

`>>>`

`incrementalize id 1`

tracks the sum/average of an entire Foldable.

`>>>`

`incrementalize id 0`

produces the latest value (ie current state is discounted to zero)

A exponential moving average with a duration of 10 (the average lag of the values effecting the calculation) is

`>>>`

`incrementalize id (1/10)`