úÎ!5«2Ë1      !"#$%&'()*+,-./0Safe" online$Most common statistics are averages.online,online takes a function and turns it into a 1G where the step is an incremental update of the (isomorphic) statistic.online moving average with a decay ratemso 'ma 1' is the simple average (no decay in the statistic), and 'ma 0.00001' is the last value (insta-decay)L.fold (ma 1) [0..100]50.0L.fold (ma 1e-12) [0..100]99.999999999999L.fold (ma 0.9) [0..100]91.00241448887785onlineabsolute averageonlineaverage squareonlinestandard deviation|The formulae for standard deviation, expressed in online terminology, highlights how this statistic is composed of averages: 9(\s ss -> sqrt (ss - s ** (one+one))) <$> ma r <*> sqma r8The average deviation of the numbers 1..1000 is about 1  sqrt 12 * 1000 (see <<https:en.wikipedia.org?wiki/Uniform_distribution_(continuous)#Standard_uniform wiki>>)L.fold (std 1) [0..1000]288.9636655359978*The average deviation with a decay of 0.99L.fold (std 0.99) [0..1000]99.28328803164005onlineDthe covariance of a tuple given an underlying central tendency foldonline/correlation of a tuple, specialised to Guassianonline/a generalised version of correlation of a tuple online\the beta in a simple linear regression of a tuple given an underlying central tendency fold onlinethe alpha of a tuple onlineÝautocorrelation is a slippery concept. This method starts with the concept that there is an underlying random error process (e), and autocorrelation is a process on top of that ie for a one-step correlation relationship.valuet = e t + k * e@t-1where k is the autocorrelation.ãThere are thus two online rates needed: one for the average being considered to be the dependent variable, and one for the online of the correlation calculation between the most recent value and the moving average. For example, L.fold (autocorr zero one)€would estimate the one-step autocorrelation relationship of the previous value and the current value over the entire sample set. onlinea constant fold   None>"´Safe-¥ onlineoA rough Median. The average absolute value of the stat is used to callibrate estimate drift towards the medianonline/onlineL1' takes a function and turns it into a 1M where the step is an incremental update of an (isomorphic) median statistic.online.onlineL1 takes a function and turns it into a 1M where the step is an incremental update of an (isomorphic) median statistic.onlineBmoving median >>> L.fold (maL1 inc d r) [1..n] 93.92822312742108onlinemoving absolute deviationonlinecovariance of a tuple onlinecorrelation of a tuple!online1the beta in a simple linear regression of a tuple"online+the alpha in a simple linear regression of 2 on 3 !"# !"#None.1y)onlinea raw non-online tdigest fold*onlinenon-online version+onlinenon-online version,online/decaying quantiles based on the tdigest library/online/decaying histogram based on the tdigest library $%&'()*+,-./ )*+$%&'(,-./None2.  !"#$%&'()*+,-./4      !"#$%&'())*+,-./0123456789:89;<#online-0.5.0-HpN3LNzCHFEI4J4JVGi8qhOnline.AveragesOnline.AveragesBOnline.MediansOnline.QuantilesOnlineAverageronlinemaabsmasqmastdcov corrGausscorrbetaalphaautocorrmconst$fMonoidAverager$fSemigroupAveragerfoldB'std'foldBstdBmaBabsmaBsqmaBMedianer medAbsSummedCount medianEst onlineL1'onlineL1maL1absmaL1covL1corrL1betaL1alphaL1 autocorrL1 OnlineTDigesttdtdNtdRatetDigesttDigestQuantiles tDigestHistonlineQuantilesmedianonlineDigitizeonlineDigestHist$fShowOnlineTDigest!foldl-1.4.6-6kFigdCLI8KusW6mJbYzf Control.FoldlFoldbase Data.Tuplesndfst