úÎL#I¸,      !"#$%&'()*+portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered)perform an analysis using surrogate data  random seed number of repetitions the evaluation function  the data zthe results, with the evaluated real data in position 1 and the rest of the array containing the evaluated surrogate data portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered)the cumulative distribution function D(x <= X)  the bins the resulting histogram mean standard deviation  the bins the resulting histogram portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Inferedcalculate a probability $a probability distribution function a PDF interface 1create a PDF from an arbtrary function f :-> [0,1] ,-.,-.portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered the entropy sum p_i lln{p_i} of a sequence the mutual information sum_x s um_y p(x,y) ln{frac{p(x,y)}{p(x)p(y)}} the underlying distribution  the sequence  the entropy the underlying distribution !the first dimension distribution "the second dimension distribution  the sequence the mutual information portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered the covariance matrix 'the correlation coefficient: (cov x y) / (std x) (std y) the mean of a list of vectors  the mean of an array of vectors .the mean of a matrix with data series in rows "the variance of a list of vectors $the variance of an array of vectors 2the variance of a matrix with data series in rows %centre the data to 0: (x - (mean x)) complementary log-log function *cloglog :: Vector Double -> Vector Double corcoeff = covariance x / (std dev x * std dev y) Dcut numerical data into intervals, data must fall inside the bounds .return the rank of each element of the vector L multiple identical entries result in the average rank of those entries (ranks :: Vector Double -> Vector Double kendall's rank correlation Ä (logit p) = log(p/(1-p)) (logit :: Vector Double -> Vector Double 2the Mahalanobis D-square distance between samples K columns are components and rows are observations (uses pseudoinverse) a list of element frequencies the p'th moment of a vector =ordinary least squares estimation for the multivariate model B Y = X B + e rows are observations, columns are elements % mean e = 0, cov e = kronecker s I compute quantiles in percent <the difference between the maximum and minimum of the input 2count the number of runs greater than or equal to n in the data !Spearman's rank correlation coefficient "centre and normalise a vector  9the dimensions of data (each vector being one dimension)  the symmetric covariance matrix  intervals data indexed by bin  the data set 6(Just sample) to be measured or use mean when Nothing D^2 moment calculate central moment calculate absolute moment data X Y :(OLS estimator for B, OLS estimator for s, OLS residuals) percentile (0 - 100) data result  longest run to count data  (run length,count) !"  !"  !"  !"portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered#9find the n principal components of multidimensional data $;perform a PCA transform of the original data (remove mean)  | Final = M^T Data^T %.perform a dimension-reducing PCA modification #$ the data the principal components the transformed data % the data eigenvalue threshold .the reduced data, with n principal components #$%#$%#$%portable provisional+haskell.vivian.mcphail <at> gmail <dot> com Safe-Infered&sigmoid transfer function '(derivative of sigmoid transfer function (remove the mean from data ) whiten data *perform an ICA transform +\ICA with default values: no dimension reduction, euclidean norms, 16 sample groups, sigmoid &'( the data (demeaned data,mean) ) the data eigenvalue threshold (whitened data,transform) * random seed !transfer function (tanh,u exp(u^2/ 2), etc...)  derivative of transfer function 0type of normalisation: Infinity, PNorm1, PNorm2 *convergence tolerance for feature vectors : -> Int -- ^ output dimensions 4sampling size (must be smaller than length of data) data  transformed data, ica transform + random seed data  transformed data, ica transform &'()*+&'()*+&'()*+/      !"#$%&'()*+,-./01234567hstatistics-0.2.3Numeric.Statistics.SurrogateNumeric.Statistics.HistogramNumeric.Statistics.PDFNumeric.Statistics.InformationNumeric.StatisticsNumeric.Statistics.PCANumeric.Statistics.ICA surrogatecumulativeToHistogramgaussianHistogramPDF probability PDFFunctionpdfFromFunctionentropymutual_informationSamplesSamplecovarianceMatrixcorrelationCoefficientMatrixmeanList meanArray meanMatrix varianceList varianceArrayvarianceMatrixcentrecloglogcorcoeffcutrankskendalllogit mahalanobismodemomentols percentilerange run_countspearman studentizepca pcaTransform pcaReducesigmoidsigmoid'demeanwhitenica icaDefaults$fPDFHistogram2D(,)$fPDFHistogramDouble$fPDFPDFFunctionb