Data.TDigest.Vector

A new data structure for accurate on-line accumulation of rank-based statistics such as quantiles and trimmed means. . See original paper: "Computing extremely accurate quantiles using t-digest" by Ted Dunning and Otmar Ertl for more details https://github.com/tdunning/t-digest/blob/master/docs/t-digest-paper/histo.pdf.

Examples

>>> quantile 0.99 (tdigest [1..1000] :: TDigest 25)
Just 990.5

>>> quantile 0.99 (tdigest [1..1000] :: TDigest 3)
Just 990.3...

t-Digest is more precise in tails, especially median is imprecise:

>>> median (forceCompress $ tdigest [1..1000] :: TDigest 10)
Just 500.5

Semigroup

This operation isn't strictly associative, but statistical variables shouldn't be affected.

>>> let td xs = tdigest xs :: TDigest 10

>>> median (td [1..500] <> (td [501..1000] <> td [1001..1500]))
Just 750.5

>>> median ((td [1..500] <> td [501..1000]) <> td [1001..1500])
Just 750.5

The linear is worst-case scenario:

>>> let td' xs = tdigest (fairshuffle xs) :: TDigest 10

>>> median (td' [1..500] <> (td' [501..1000] <> td' [1001..1500]))
Just 750.5

>>> median ((td' [1..500] <> td' [501..1000]) <> td' [1001..1500])
Just 750.5

Construction

data TDigest (compression :: Nat)

TDigest is a vector of centroids plus not yet merged elements.

The size of structure is dictated by compression, *𝛿*. And is *O(𝛿)*.

Instances

KnownNat comp => Reducer Double (TDigest comp)

Both cons and snoc are insert

Defined in Data.TDigest.Vector.Internal

Methods

unit :: Double -> TDigest comp

snoc :: TDigest comp -> Double -> TDigest comp

cons :: Double -> TDigest comp -> TDigest comp

Show (TDigest compression)

Defined in Data.TDigest.Vector.Internal

Methods

showsPrec :: Int -> TDigest compression -> ShowS

show :: TDigest compression -> String

showList :: [TDigest compression] -> ShowS

KnownNat comp => Semigroup (TDigest comp)

Defined in Data.TDigest.Vector.Internal

Methods

(<>) :: TDigest comp -> TDigest comp -> TDigest comp

sconcat :: NonEmpty (TDigest comp) -> TDigest comp

stimes :: Integral b => b -> TDigest comp -> TDigest comp

KnownNat comp => Monoid (TDigest comp)

Defined in Data.TDigest.Vector.Internal

Methods

mempty :: TDigest comp

mappend :: TDigest comp -> TDigest comp -> TDigest comp

mconcat :: [TDigest comp] -> TDigest comp

NFData (TDigest comp)

Defined in Data.TDigest.Vector.Internal

Methods

rnf :: TDigest comp -> ()

KnownNat comp => HasHistogram (TDigest comp) Maybe

Defined in Data.TDigest.Vector.Internal

Methods

histogram :: TDigest comp -> Maybe (NonEmpty HistBin)

totalWeight :: TDigest comp -> Weight

tdigest :: (Foldable f, KnownNat comp) => f Double -> TDigest comp

Strict foldl' over Foldable structure.

Population

singleton :: Double -> TDigest comp

Make a TDigest of a single data point.

insert

Arguments

:: KnownNat comp

=> Double

element

-> TDigest comp

-> TDigest comp

Insert single value into TDigest.

insert'

Arguments

:: KnownNat comp

=> Double

element

-> TDigest comp

-> TDigest comp

Insert single value, don't compress TDigest even if needed.

This may violate the insertion buffer size invariant.

For sensibly bounded input, it makes sense to let TDigest grow (it might grow linearly in size), and after that compress it once.

Compression

>>> let digest = foldl' (flip insert') mempty [0..1000] :: TDigest 5
>>> (size digest, size $ compress digest)
(1001,173)

>>> (quantile 0.1 digest, quantile 0.1 $ compress digest)
(Just 99.6...,Just 99.6...)

compress :: forall comp. KnownNat comp => TDigest comp -> TDigest comp

forceCompress :: forall comp. KnownNat comp => TDigest comp -> TDigest comp

Statistics

minimumValue :: KnownNat comp => TDigest comp -> Mean

Center of left-most centroid. Note: may be different than min element inserted.

>>> minimumValue (tdigest [1..100] :: TDigest 3)
1.0

maximumValue :: KnownNat comp => TDigest comp -> Mean

Center of right-most centroid. Note: may be different than max element inserted.

>>> maximumValue (tdigest [1..100] :: TDigest 3)
100.0

Percentile

median :: KnownNat comp => TDigest comp -> Maybe Double

Median, i.e. quantile 0.5.

quantile :: KnownNat comp => Double -> TDigest comp -> Maybe Double

Calculate quantile of a specific value.

Mean & Variance

>>> stddev (tdigest $ fairshuffle [0..100] :: TDigest 10)
Just 29.0...

mean :: KnownNat comp => TDigest comp -> Maybe Double

Mean.

>>> mean (tdigest [1..100] :: TDigest 10)
Just 50.5

Note: if you only need the mean, calculate it directly.

variance :: KnownNat comp => TDigest comp -> Maybe Double

Variance.

stddev :: KnownNat comp => TDigest comp -> Maybe Double

Standard deviation, square root of variance.

CDF

cdf :: KnownNat comp => Double -> TDigest comp -> Double

Cumulative distribution function.

Note: if this is the only thing you need, it's more efficient to count this directly.

icdf :: KnownNat comp => Double -> TDigest comp -> Maybe Double

An alias for quantile

Debug

size :: TDigest comp -> Int

Size of structure

valid :: TDigest comp -> Bool

isRight . validate

validate :: TDigest comp -> Either String (TDigest comp)

Check various invariants in the TDigest structure.