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README
foldlstatistics
A reimplementation of the Statistics.Sample
module using the foldl package.
The intention of this package is to allow these algorithms to be used on a much broader set of data input types,
including lists and streaming libraries such as conduit
and pipes
, and any other type which is Foldable
.
All statistics in this package can be computed with no more than two passes over the data  once to compute the mean and once to compute
any statistics which require the mean. this is achieved because foldl Fold
s are Applicative
, which means that to compute, for example, the first 4 central moments as well as the count, the following could be used:
import Control.Foldl as F
...
dataseries :: [Double]
dataseries = ...
...
let m = F.fold mean dataseries
(c2,c3,c4,c5,n) = flip F.fold dataseries $
(\(c2,c3) (c4,c5) n > (c2,c3,c4,c5,n))
<$> centralMoment 2 3 m
<*> centralMoment 4 5 m
<*> F.length
which traverses the data twice, once to compute the mean m
, and once to compute all the central moments and the count concurrently. This brings along with it for free the ability to compute streaming statistics, such as the mean of all data seen so far, using the foldl
's scan
function.
Where possible, care has been taken to ensure the numerical stability of the computation of statistics.
Several algorithms require the mean of the data to be known before computing the statistic, such as skewness
, kurtosis
and other centralMoment
s.
There are 'fast' implementations for calculating the variance, unbiased variance and standard deviation, which can be computed without knowing the mean
a priori, but which may produce less accurate results.
Performance & Correctness
Benchmarks are included comparing performance to the statistics package. In nearly all cases, the implementations in this package perform better than those in statistics
on the same inputs, and in several cases, performing two passes (to compute the mean and another statistic) is faster than the equivalent statistics
implementation.
This speed has not come at the cost of correctness; all Fold
s are tested against their statistics
counterparts to ensure the results are identical.
These results can be confirmed by running
stack build test bench benchmarkarguments "output bench.html"
which will print out the results of the tests against statistics
and then run the benchmark (this may take several minutes and is best run on a "quiet" machine which is doing very little other than running the benchmark). The results of the benchmarking are then available in the file bench.html
.