Safe Haskell	None
Language	Haskell2010

Math.Probable.Distribution

Contents

Common distributions
Finite distributions
Utility functions

Synopsis

Common distributions

beta Source #

Arguments

:: PrimMonad m
=> Double	shape parameter alpha
-> Double	shape parameter beta
-> RandT m Double

Beta distribution (from Statistics.Distribution.Beta)

λ> mwc $ listOf 10 (beta 81 219)
[ 0.23238372272745833,0.252972980515086,0.22708315774257903
, 0.25807200295967214,0.29794072226119983,0.24534701159196015
, 0.24766870269839578,0.2994199351220346,0.2728157476212405,0.2593318159573564
]

cauchy Source #

Arguments

:: PrimMonad m
=> Double	central point
-> Double	scale parameter
-> RandT m Double

Cauchy distribution (from Statistics.Distribution.Cauchy)

λ> mwc $ listOf 10 (cauchy 0 0.1)
[ -0.3932758718373347,0.490467375093784,4.2620417667423555e-2
, 3.370509874905657e-2,-8.186484692937862e-2,9.371858212168262e-2
, -1.1095818809115384e-2,3.0353983716155386e-2,0.22759697862410477
, -0.1881828277028582 ]

cauchyStd :: PrimMonad m => RandT m Double Source #

Cauchy distribution around 0, with scale 1 (from Statistics.Distribution.Cauchy)

λ> mwc $ listOf 10 cauchyStd
[ 9.409701589649838,-7.361963972107541,0.168746305673769
, 5.091825420838711,-0.326080163135388,-1.2989850787629456
, -2.685658063444485,0.22671438734899435,-1.602349559644217e-2
, -0.6476292643908057 ]

chiSquared Source #

Arguments

:: PrimMonad m
=> Int	number of degrees of freedom
-> RandT m Double

Chi-squared distribution (from Statistics.Distribution.ChiSquared)

λ> mwc $ listOf 10 (chiSquare 4)
[ 8.068852054279787,1.861584389294606,6.3049415103095265
, 1.0512164068833838,1.6243237867165086,5.284901049954076
, 0.4773242487947021,1.1753876666374887,5.21554771873363
, 3.477574639460651 ]

fisher :: PrimMonad m => Int -> Int -> RandT m Double Source #

Fisher's F-Distribution (from Statistics.Distribution.FDistribution)

λ> mwc $ listOf 10 (fisher 4 3)
[ 3.437898578540642,0.844120450719367,1.9907851466347173
, 2.0089975147012784,1.3729208790549117,0.9380430357924707
, 2.642389323945247,1.0918121624055352,0.45650856735477335
, 2.5134537326659196 ]

gamma Source #

Arguments

:: PrimMonad m
=> Double	shape parameter k
-> Double	scale parameter theta
-> RandT m Double

Gamma distribution (from Statistics.Distribution.Gamma)

λ> mwc $ listOf 10 (gamma 3 0.1)
[ 5.683745415884202e-2,0.20726188766138176,0.3150672538487696
, 0.4250825346490057,0.5586516230326105,0.46897413151474315
, 0.18374916962208182,9.93000480494153e-2,0.6057279704154832
, 0.11070190282993911 ]

improperGamma Source #

Arguments

:: PrimMonad m
=> Double	shape parameter k
-> Double	scale parameter theta
-> RandT m Double

Gamma distribution, without checking whether the parameter are valid (from Statistics.Distribution.Gamma)

λ> mwc $ listOf 10 (improperGamma 3 0.1)
[ 0.30431838005485,0.4044380297376584,2.8950141419406657e-2
, 0.468271612850147,0.18587792578128381,0.22735854572527045
, 0.5168050216325927,5.896911236207261e-2,0.24654560998405564
, 0.10557650513145429 ]

geometric Source #

Arguments

:: PrimMonad m
=> Double	success rate
-> RandT m Int

Geometric distribution.

Distribution of the number of trials needed to get one success. See Statistics.Distribution.Geometric

λ> mwc $ listOf 10 (geometric 0.8)
[2,1,1,1,1,1,1,2,1,5]

geometric0 :: PrimMonad m => Double -> RandT m Int Source #

Geometric distribution.

Distribution of the number of failures before getting one success. See Statistics.Distribution.Geometric

λ> mwc $ listOf 10 (geometric0 0.8)
[0,0,0,0,0,1,1,0,0,0]

student :: PrimMonad m => Double -> RandT m Double Source #

Student-T distribution (from Statistics.Distribution.StudentT)

λ> mwc $ listOf 10 (student 0.2)
[ -14.221373473810829,-29.395749168822267,19.448665112984997
, -30.00446058929083,-0.5033202547957609,2.321975597874013
, 0.7884787761643617,-0.1895113832448149,-131.12901170537924
, 1.371956948317759 ]

uniform :: PrimMonad m => Double -> Double -> RandT m Double Source #

Uniform distribution between a and b (from Statistics.Distribution.Uniform)

λ> mwc $ listOf 10 (uniform 0.1 0.2)
[ 0.1711914559256124,0.1275212181343327,0.15347702635758945
, 0.1743662387063698,0.12047749686635312,0.10719840237585587
, 0.10543681342025846,0.13482973080648325,0.19779298960413577
, 0.1681037592576508 ]

normal Source #

Arguments

:: PrimMonad m
=> Double	mean
-> Double	standard deviation
-> RandT m Double

Normal distribution (from Statistics.Distribution.Normal)

λ> mwc $ listOf 10 (normal 4 1)
[ 3.6815394812555144,3.5958531529526727,3.775960990625964
, 4.413109650155896,4.825826384709198,4.805629590118984
, 5.259267547365003,4.45410634165052,4.886537243027636
, 3.0409409067356954 ]

standard :: PrimMonad m => RandT m Double Source #

The standard normal distribution (mean = 0, stddev = 1) (from Statistics.Distribution.Normal)

λ> mwc $ listOf 10 standard
[ 0.2252627935262769,1.1831885443897947,-0.6577353418647461
, 2.1574536855051853,-0.16983072710637676,0.9667954287638821
, -1.8758605246293683,-0.8578048838241616,1.9516838769731923
, 0.43752574431460434 ]

normalFromSample Source #

Arguments

:: PrimMonad m
=> Sample	sample
-> Maybe (RandT m Double)

Create a normal distribution using parameters estimated from the sample (from Statistics.Distribution.Normal)

λ> mwc . listOf 10 $ 
     normalFromSample $ 
       V.fromList [1,1,1,3,3,3,4
                  ,4,4,4,4,4,4,4
                  ,4,4,4,4,4,5,5
                  ,5,7,7,7]
[ 7.1837511677441395,2.388433817342809,5.252282321156134
, 4.988163140851522,0.40102386713467864,4.4840751065620665
, 2.1471370686776874,2.6591948802201046,3.843667372514598
, 1.7650436484843248 ]

exponential Source #

Arguments

:: PrimMonad m
=> Double	lambda (scale) parameter
-> RandT m Double

Exponential distribution (from Statistics.Distribution.Exponential)

λ> mwc $ listOf 10 (exponential 0.2)
[ 5.713524665694821,1.7774315204594584,2.434017573227628
, 5.463202731505528,0.5403008025455847,14.346316301765576
, 7.380393612391503,24.800854500680032,0.8731076703020924
, 6.1661076502236645 ]

exponentialFromSample :: PrimMonad m => Sample -> Maybe (RandT m Double) Source #

Exponential distribution given a sample (from Statistics.Distribution.Exponential)

λ> mwc $ listOf 10 (exponentialFromSample $ V.fromList [1,1,1,0])
[ 0.4237050903604833,1.934301502525168,0.7435728843566659
, 1.8720263209574293,0.605750265970631,0.24103955067365979
, 0.6294952762436511,1.660404952631443,0.6448230847113577
, 0.8891555734786789 ]

Finite distributions

module Math.Probable.Distribution.Finite

Utility functions

continuous Source #

Arguments

:: (ContGen d, PrimMonad m)
=> d	the continuous distribution to sample from
-> RandT m Double

Sample from a continuous distribution from the statistics package

λ> import qualified Statistics.Distribution.Normal as Normal
λ> mwc $ continuous (Normal.normalDistr 0 1)
-0.7266583064693862

This is equivalent to using normal from this module.

discrete Source #

Arguments

:: (DiscreteGen d, PrimMonad m)
=> d	the discrete distribution to sample from
-> RandT m Int

Sample from a discrete distribution from the statistics package

λ> import qualified Statistics.Distribution.Normal as Normal
λ> mwc $ discrete (Geo.geometric 0.6)
2

This is equivalent to using geometric from this module.