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The Nematrian Function Library

Statistical Functions

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The Nematrian function library includes a range of tools that are useful for carrying out statistical calculations.

 

The web functions available include ones set out in the table below. To see a complete list of functions currently available in the Nematrian online toolkit please go to list of types of available functions or complete list of individual functions.

 


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Web functionShort description of function
MnApplyGeometricSpreadToSeriesReturns a series formed by applying a geometric spread to another series
MnArithmeticallySpacedArrayReturns a series whose elements are equally spaced (arithmetically)
MnBinomialCdfReturns the value of the cumulative distribution function for the binomial distribution
MnBinomialPmfReturns the value of the probability mass function for the binomial distribution
MnBivariateNormalDistributionReturns the value of the cumulative unit bivariate normal distribution function
MnBlendedPCAICAReturns the blended principal components/independent components extracted from several simultaneous data series
MnBoxCoxSeriesTransformReturns the Box-Cox transform of a series
MnChiDistReturns the right tail cumulative distribution function (i.e. 1 - cdf) for the chi-squared distribution
MnChiInvReturns the right tail inverse cdf (i.e. quantile of 1-q) of the chi-squared distribution
MnChiSqDistCdfReturns the cumulative distribution function for the chi-squared distribution
MnChiSqDistPdfReturns the probability density function of the chi-squared distribution
MnChiSqInvReturns the inverse cdf, i.e. quantile, of the chi-squared distribution
MnChiSqTestReturns the confidence level applicable to a chi-squared statistical test
MnChiSqTestDoFReturns the number of degrees of freedom applicable to a chi-squared statistical test
MnChiSqTestStatisticReturns the test statistic of a chi-squared statistical test
MnCholeskyDecompositionReturns the Cholesky decomposition of a square matrix
MnConfidenceLevelKurtApproxIfNormalReturns the (approx) confidence level for sample skew, under null hypothesis that distribution is Normal
MnConfidenceLevelSkewApproxIfNormalReturns the (approx) confidence level for sample skew, under null hypothesis that distribution is Normal
MnConfidenceNormReturns the confidence interval for a population mean, using a normal distribution
MnConfidenceTReturns the confidence interval for a population mean, using a Student's t distribution
MnConvert2dIndexArrayToLogRelativeReturnsReturns an array of logged relative returns from an array of index values (for several different series simultaneously)
MnConvert2dIndexArrayToLogReturnsReturns an array of logged returns from an array of index values (for several different series simultaneously)
MnConvert2dIndexArrayToRelativeReturnsReturns an array of relative returns from an array of index values (for several different series simultaneously)
MnConvert2dIndexArrayToReturnsReturns an array of returns from an array of index values (for several different series simultaneously)
MnCorrelationReturns the (Pearson) correlation coefficient between two series
MnCorrelationsReturns an array corresponding to the m x m elements of the correlation matrix
MnCovarianceReturns the (sample) covariance between two series
MnCovariancesReturns an array corresponding to the m x m elements of the (sample) covariance matrix
MnCumulativeNormalReturns the value of the cumulative unit normal distribution function for a given distribution point
MnCumulativeSeriesReturns the cumulative values of an ordered series
MnDAAnovaOneAnalysisReturns the results of a one factor Analysis of Variance
MnDAAnovaOneSummaryReturns summary of input data applicable to a one factor Analysis of Variance
MnDAAnovaTwoWithAnalysisReturns the results of a two factor Analysis of Variance (with replication)
MnDAAnovaTwoWithoutAnalysisReturns the results of a two factor Analysis of Variance (without replication)
MnDAAnovaTwoWithoutSummaryReturns summary of input data applicable to a two factor Analysis of Variance (without replication)
MnDAAnovaTwoWithSummaryReturns summary of input data applicable to a two factor Analysis of Variance (with replication)
MnDACorrelationsReturns the (lower triangular) correlation matrix between a collection of series
MnDACovariancesReturns the (lower triangular) (population) covariance matrix between a collection of series
MnDAExponentialSmoothingReturns the result of applying an exponential smoothing to a data series
MnDAFTestReturns the result of applying an F test to two series
MnDAMovingAverageReturns the result of applying a moving average algorithm to a data series
MnDATTestEqualReturns the result of applying a Student's t test to test if two different data have means that differ by a set amount, assuming that they have equal variance
MnDATTestPairedReturns the result of applying a Student's t test to the difference of paired data
MnDATTestUnequalReturns the result of applying a Student's t test to test if two different data have means that differ by a set amount, assuming that they have unequal variance
MnDAZTestReturns the result of applying a z test to test if two different data have means that differ by a set amount, assuming that they have known variances
MnDesmooth_AR1Returns an array of desmoothed values
MnDesmooth_AR1_rhoReturns desmoothing parameter for an array
MnDoesArrayHaveModeReturns true if the array has a unique mode (i.e. a value which it takes more than any others), otherwise returns false
MnExponDistCdfReturns the cumulative distribution function of the exponential distribution
MnExponDistPdfReturns the probability density function of the exponential distribution
MnFDistCdfReturns the cumulative distribution function for the F distribution
MnFDistPdfReturns the probability density function of the F distribution
MnFInvReturns the inverse cdf, i.e. quantile, of the F distribution
MnForecastReturns the predicted value from a linear regression exercise
MnFTestReturns the result of an F-test to determine the probability of the F-statistic being less than the observed statistic
MnGammaDistCdfReturns the cumulative distribution function of the gamma distribution
MnGammaDistPdfReturns the probability density function of the gamma distribution
MnGammaInvReturns the inverse cdf, i.e. quantile, of the gamma distribution
MnGaussReturns the Gauss function, i.e. the cumulative (standard) normal function less 0.5
MnHaltonSequenceReturns a Halton quasi-random sequence
MnHerfindahlHirschmanIndexReturns the Herfindahl-Hirshmann Index (HHI) of an array of (non-negative) market shares
MnInterceptReturns the intercept from a linear regression exercise
MnInverseNormalReturns the inverse of the cumulative unit normal function
MnKendalTauCoefficientReturns the Kendal tau coefficientbetween two series
MnKendalTauCoefficientsReturns an array corresponding to m x m Kendal tau coefficients between m series
MnKurtReturns the kurtosis of an array
MnLeastSquaresGeneralisedCurveFitReturns an array corresponding to values of a least squares generalised curve fit of input data
MnLeastSquaresPolynomialCurveFitReturns an array corresponding to values of a least squares polynomial curve fit of input data
MnLognormDistCdfReturns the cumulative distribution function of the lognormal distribution
MnLognormDistPdfReturns the probability density function of the lognormal distribution
MnLognormInvReturns the inverse cdf, i.e. quantile, of the lognormal distribution
MnMaximumOfArrayReturns the maximum of an array of values
MnMaximumOfDateArrayReturns the maximum of an array of dates
MnMeanReturns the mean of an array
MnMeanAbsDevVsMeanReturns the mean absolute deviation (versus the mean) of an array
MnMeanAbsDevVsMedianReturns the mean absolute deviation (versus the median) of an array
MnMedianReturns the median of an array
MnMinimumOfArrayReturns the minimum of an array of values
MnMinimumOfDateArrayReturns the minimum of an array of dates
MnModeOfArrayReturns the mode of an array (if it exists)
MnMultiplySeriesByConstantReturns the result of multiplying two series term-by-term
MnMultiplyTwoSeriesElementByElementReturns the result of multiplying two series term-by-term
MnNormaliseArrayReturns the Normalised equivalent of the input array
MnNormaliseWeightedArrayReturns the (weighted) Normalised equivalent of the input array
MnNormalMLFitReturns maximum likelihood estimates of mean and standard devation of Normally distributed observations
MnNormalTailFitReturns least squares tail fit estimates of mean and standard devation of Normally distributed observations
MnPercentileReturns a given percentile point for an array with lowest value deemed to be 0'th percentile and highest 1'th percentile
MnPercentileExcReturns a given percentile point for an array with lowest value deemed to be 1/(n+1)'th percentile and highest n/(n+1)'th percentile
MnPoissonCdfReturns the cumulative distribution function of the poisson distribution
MnPoissonPmfReturns the probability mass function of the poisson distribution
MnPopulationCovarianceReturns the population covariance between two series
MnPopulationCovariancesReturns an array corresponding to the m x m elements of the population covariance matrix
MnPopulationKurtReturns the (population) (excess) kurtosis of an array
MnPopulationSkewReturns the (population) skew of an array
MnPopulationStdevReturns the (population) standard deviation of an array
MnPopulationVarianceReturns the (population) variance of an array
MnPrincipalComponentsReturns the principal components extracted from several simultaneous data series
MnPrincipalComponentsSizesReturns the sizes of the principal components extracted from several simultaneous data series
MnPrincipalComponentsWeightsReturns the weights ascribed to the principal components extracted from several simultaneous data series
MnQuartileReturns a given quantile point for an array (quart = 0, 1, 2, 3 or 4) with lowest value deemed to be 0'th percentile and highest 1'th percentile
MnQuartileExcReturns a given quantile point for an array (quart = 1, 2, 3) with lowest value deemed to be 1/(n+1)'th percentile and highest n/(n+1)'th percentile
MnRandReturns a uniform random number between 0 and 1
MnRandBetweenReturns a uniform (integral) random number between bottom and top
MnRelativeVolUsingCorrReturns the relative risk (volatility) of a portfolio versus a benchmark from correlations
MnRelativeVolUsingCovReturns the relative risk (volatility) of a portfolio versus a benchmark from covariances
MnReorderSeriesReturns InputArray but reordered as per IndexArray
MnRSqReturns the r-squared for a regression between known y's and known x's
MnSkewReturns the skewness of an array
MnSlopeReturns the slope from a linear regression exercise
MnSpearmanRankCorrelationReturns the Spearman rank correlation coefficient between two series
MnSpearmanRankCorrelationsReturns an array corresponding to the m x m elements of the Spearman rank correlation matrix
MnStandardisedNormalQuantilesReturns an array of standardised normal quantile points
MnStandardWeightedCubicQuantileFitReturns an array giving a 'standard' weighted cubic quantile fit to a series of values
MnStandardWeightedCubicQuantileFitInclEndsReturns an array giving a 'standard' weighted cubic quantile fit to a series of values
MnStdevReturns the (sample) standard deviation of an array
MnTDistCdfReturns the cumulative distribution function of the Student's t distribution
MnTDistPdfReturns the probability density function of the Student's t distribution
MnTInvReturns the inverse cdf, i.e. quantile, of the Student's t distribution
MnTrailingVolatilityAdjustArrayReturns a new array derived by adjusting the InputArray by the volatility (stdev) of the preceding TrailPeriod entries
MnUnitNormalDensityReturns the unit normal density (i.e. mass) function. The unit Normal distribution has a mean of 0 (zero) and a standard deviation of 1 (one)
MnVarianceReturns the (sample) variance of an array
MnWeightedCorrelationReturns the weighted correlation between two series
MnWeightedCorrelationsReturns an array consisting of the m x m entries in the weighted correlation coefficient matrix
MnWeightedCovarianceReturns the weighted (sample) covariance between two series
MnWeightedCovariancesReturns an array consisting of the m x m entries in the weighted (sample) covariance matrix
MnWeightedDesmooth_AR1Returns an array of desmoothed values (giving different weights to different observations)
MnWeightedDesmooth_AR1_rhoReturns desmoothing parameter for an array (giving different weights to different observations)
MnWeightedMeanReturns the weighted mean of an array
MnWeightedMeanAbsDevVsMeanReturns the weighted mean absolute deviation (versus the mean) of an array
MnWeightedMeanAbsDevVsMedianReturns the weighted mean absolute deviation (versus the median) of an array
MnWeightedMedianReturns the weighted median of an array
MnWeightedPercentileReturns the weighted percentile of an array
MnWeightedPopulationCovarianceReturns the weighted population covariance matrix between two series
MnWeightedPopulationCovariancesReturns an array consisting of the m x m entries in the weighted population covariance matrix
MnWeightedPopulationKurtReturns the weighted population (excess) kurtosis of an array
MnWeightedPopulationSkewReturns the weighted population skew of an array
MnWeightedPopulationStdevReturns the weighted population standard deviation of an array
MnWeightedPopulationVarianceReturns the weighted population variance of an array
MnWeightedSkewReturns the weighted skew of an array
MnWeightedSpearmanRankCorrelationReturns the weighted Spearman rank correlation coefficient between two series
MnWeightedStdevReturns the weighted (sample) standard deviation of an array
MnWeightedVarianceReturns the weighted (sample) variance of an array

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