Portability | Haskell 2011 + TypeFamilies |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | Safe-Infered |
- newtype L r = L {}
- (@@) :: (Num r, Ord r) => L r -> [r] -> r
- (@!) :: Num r => L r -> Vector r -> r
- (@#) :: Num r => L r -> Int -> [r]
- breakdown :: (Num r, Eq r) => L r -> Int
- trimean :: Fractional r => L r
- midhinge :: Fractional r => L r
- iqr :: Fractional r => L r
- iqm :: Fractional r => L r
- lscale :: Fractional r => L r
- trimmed :: Fractional r => Rational -> L r -> L r
- winsorized, winsorised :: Fractional r => Rational -> L r -> L r
- jackknifed :: Fractional r => L r -> L r
- mean :: Fractional r => L r
- total :: Num r => L r
- lmin :: Num r => L r
- lmax :: Num r => L r
- midrange :: Fractional r => L r
- nthSmallest :: Num r => Int -> L r
- nthLargest :: Num r => Int -> L r
- quantile :: Fractional r => Rational -> L r
- median :: Fractional r => L r
- tercile :: Fractional r => Rational -> L r
- t1, t2 :: Fractional r => L r
- quartile :: Fractional r => Rational -> L r
- q1, q3, q2 :: Fractional r => L r
- quintile :: Fractional r => Rational -> L r
- qu1, qu4, qu3, qu2 :: Fractional r => L r
- percentile :: Fractional r => Rational -> L r
- permille :: Fractional r => Rational -> L r
- hdquantile :: Fractional r => Rational -> L r
- quantileBy :: Num r => Estimator r -> Rational -> L r
- type Estimator r = Rational -> Int -> Estimate r
- data Estimate r = Estimate !Rational (IntMap r)
- r1 :: Num r => Estimator r
- r2 :: Fractional r => Estimator r
- r3 :: Num r => Estimator r
- r4 :: Fractional r => Estimator r
- r5 :: Fractional r => Estimator r
- r6 :: Fractional r => Estimator r
- r7 :: Fractional r => Estimator r
- r8 :: Fractional r => Estimator r
- r9 :: Fractional r => Estimator r
- r10 :: Fractional r => Estimator r
L-Estimator
L-estimators are linear combinations of order statistics used by robust
statistics.
Num r => VectorSpace (L r) | |
Num r => AdditiveGroup (L r) |
Applying an L-estimator
(@@) :: (Num r, Ord r) => L r -> [r] -> rSource
Calculate the result of applying an L-estimator after sorting list into order statistics
(@!) :: Num r => L r -> Vector r -> rSource
Calculate the result of applying an L-estimator to a *pre-sorted* vector of order statistics
Analyzing an L-estimator
(@#) :: Num r => L r -> Int -> [r]Source
get a vector of the coefficients of an L estimator when applied to an input of a given length
Robust L-Estimators
trimean :: Fractional r => L rSource
Tukey's trimean
breakdown trimean = 25
midhinge :: Fractional r => L rSource
midhinge = trimmed 0.25 midrange breakdown midhinge = 25%
iqr :: Fractional r => L rSource
interquartile range
breakdown iqr = 25% iqr = trimmed 0.25 midrange
iqm :: Fractional r => L rSource
interquartile mean
iqm = trimmed 0.25 mean
lscale :: Fractional r => L rSource
Direct estimator for the second L-moment given a sample
L-Estimator Combinators
trimmed :: Fractional r => Rational -> L r -> L rSource
Calculate a trimmed L-estimator. If the sample size isn't evenly divided, linear interpolation is used as described in http://en.wikipedia.org/wiki/Trimmed_mean#Interpolation
winsorized, winsorised :: Fractional r => Rational -> L r -> L rSource
Calculates an interpolated winsorized L-estimator in a manner analogous to the trimmed estimator. Unlike trimming, winsorizing replaces the extreme values.
jackknifed :: Fractional r => L r -> L rSource
Jackknifes the statistic by removing each sample in turn and recalculating the L-estimator, requires at least 2 samples!
Trivial L-Estimators
mean :: Fractional r => L rSource
The average of all of the order statistics. Not robust.
breakdown mean = 0%
midrange :: Fractional r => L rSource
midrange = lmax - lmin breakdown midrange = 0%
Sample-size-dependent L-Estimators
nthSmallest :: Num r => Int -> L rSource
nthLargest :: Num r => Int -> L rSource
Quantiles
Common quantiles
quantile :: Fractional r => Rational -> L rSource
Compute a quantile with traditional direct averaging
median :: Fractional r => L rSource
The most robust L-estimator possible.
breakdown median = 50
tercile :: Fractional r => Rational -> L rSource
t1, t2 :: Fractional r => L rSource
terciles 1 and 2
breakdown t1 = breakdown t2 = 33%
quartile :: Fractional r => Rational -> L rSource
q1, q3, q2 :: Fractional r => L rSource
quantiles, with breakdown points 25%, 50%, and 25% respectively
quintile :: Fractional r => Rational -> L rSource
percentile :: Fractional r => Rational -> L rSource
breakdown (percentile n) = min n (100 - n)
permille :: Fractional r => Rational -> L rSource
Harrell-Davis Quantile Estimator
hdquantile :: Fractional r => Rational -> L rSource
The Harrell-Davis quantile estimate. Uses multiple order statistics to approximate the quantile to reduce variance.
Compute a quantile using a specified quantile estimation strategy
quantileBy :: Num r => Estimator r -> Rational -> L rSource
Compute a quantile using the given estimation strategy to interpolate when an exact quantile isn't available
Sample Quantile Estimators
r2 :: Fractional r => Estimator rSource
.. with averaging at discontinuities
r3 :: Num r => Estimator rSource
The observation numbered closest to Np. NB: does not yield a proper median
r4 :: Fractional r => Estimator rSource
Linear interpolation of the empirical distribution function. NB: does not yield a proper median.
r5 :: Fractional r => Estimator rSource
.. with knots midway through the steps as used in hydrology. This is the simplest continuous estimator that yields a correct median
r6 :: Fractional r => Estimator rSource
Linear interpolation of the expectations of the order statistics for the uniform distribution on [0,1]
r7 :: Fractional r => Estimator rSource
Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]
r8 :: Fractional r => Estimator rSource
Linear interpolation of the approximate medans for order statistics.
r9 :: Fractional r => Estimator rSource
The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed.
r10 :: Fractional r => Estimator rSource
When rounding h, this yields the order statistic with the least expected square deviation relative to p.