úÎ)Ã'Í"      ! experimental,Alexey Khudyakov <alexey.skladnoy@gmail.com><Monoid which allows to calculate two statistics in parralel @Monoid which corresponds to some stattics. In order to do so it ( must be commutative. In many cases it's not practical to ) construct monoids for each element so papennd was added. D First parameter of type class is monoidal accumulator. Second is 8 type of element over which statistic is calculated. ;Statistic could be calculated with fold over sample. Since  accumulator is ") such fold could be easily parralelized. %Instance must satisfy following law:  M pappend x (pappend y mempty) == pappend x mempty `mappend` pappend y mempty  mappend x y == mappend y x BIt is very similar to Reducer type class from monoids package but  require commutative monoids =Add one element to monoid accumulator. P stands for point in  analogy for Pointed. Calculate statistic over Foldable. It's implemented in terms of  foldl'. ,Data type which could be convered to Double  &Calculate biased estimate of variance 7Calculate unbiased estimate of the variance, where the  denominator is $n-1$. &Calculate esimate of mean of a sample Number of elements in sample ?Calculate maximum of sample. For empty sample returns NaN. Any $ NaN encountedred will be ignored. ?Calculate minimum of sample. For empty sample returns NaN. Any $ NaN encountedred will be ignored. =Intermediate quantities to calculate the standard deviation. >Mean of sample. Samples of Double,Float and bui;t-in integral  types are supported Numeric stability of # is not proven. 6Simplest statistics. Number of elements in the sample Fix type of monoid Fix type of monoid Fix type of monoid BCalculate sample standard deviation (biased estimator, $s$, where  the denominator is $n-1$). !+Calculate standard deviation of the sample  (unbiased estimator, $s&igma$, where the denominator is $n$). $%Using parallel algorithm from: ;Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1979), A Updating Formulae and a Pairwise Algorithm for Computing Sample < Variances., Technical Report STAN-CS-79-773, Department of 0 Computer Science, Stanford University. Page 4.  Iftp://reports.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf   ! !    !&      ! "#$%monoid-statistics-0.2Data.Monoid.StatisticsData.Monoid.Statistics.NumericTwoStats calcStat1 calcStat2 StatMonoidpappend evalStatisticConvertibleToDoubletoDouble CalcVariance calcVariancecalcVarianceUnbiasedCalcMeancalcMean CalcCount calcCountMaxcalcMaxMincalcMinVarianceMeanCount calcCountIasCountasMean asVariance calcStddevcalcStddevUnbiasedbase Data.MonoidMonoidmappendsqr$fMonoidVariance