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Statistics

The Statistics module provides tools for analyzing and summarizing data in Nelson.

It includes functions for computing measures of central tendency, variability, correlation, and probability distributions.

The module also supports advanced data summarization structures for accurate quantile estimation, enabling robust statistical analysis and interpretation of datasets.

Descriptive Statistics and Visualization

Functions for summarizing, exploring, ranking, and visualizing statistical data.

  • bootci
    Bootstrap confidence interval.
  • bootstrp
    Bootstrap sampling.
  • corr
    Linear or rank correlation.
  • corrcoef
    Correlation coefficients
  • cov
    Covariance
  • crosstab
    Cross-tabulation.
  • ecdf
    Empirical cumulative distribution function.
  • geomean
    Geometric mean of a data set.
  • harmmean
    Harmonic mean of a data set.
  • hist
    Histogram bin counts.
  • histfit
    Histogram with fitted distribution curve.
  • iqr
    Interquartile range.
  • jackknife
    Jackknife statistics.
  • ksdensity
    Kernel smoothing function estimate.
  • kurtosis
    Kurtosis of a data set.
  • mad
    Mean or median absolute deviation.
  • mean
    Mean of array elements.
  • median
    Median value of array elements.
  • mode
    Most frequent values.
  • moment
    Central moment of a data set.
  • nanmax
    Maximum, ignoring NaN values.
  • nanmean
    Mean, ignoring NaN values.
  • nanmedian
    Median, ignoring NaN values.
  • nanmin
    Minimum, ignoring NaN values.
  • nanstd
    Standard deviation, ignoring NaN values.
  • nansum
    Sum, ignoring NaN values.
  • nanvar
    Variance, ignoring NaN values.
  • prctile
    Percentiles of a data set.
  • probplot
    Probability plot.
  • qqplot
    Quantile-quantile plot.
  • quantile
    Quantiles of a data set.
  • range
    Range of values.
  • skewness
    Skewness of a data set.
  • std
    Standard deviation
  • tabulate
    Frequency table.
  • tdigest
    t-digest algorithm data structure for accurate quantile estimation with configurable compression parameters
  • tiedrank
    Ranks with average values for ties.
  • trimmean
    Mean after trimming extreme values.
  • var
    Variance
  • zscore
    Standardized z-scores.
Probability Distributions

Distribution functions for density, cumulative probability, inverse probability, fitting, likelihood, random sampling, and summary statistics.

  • betacdf
    Beta cumulative distribution function
  • betafit
    Beta parameter estimates
  • betainv
    Beta inverse cumulative distribution function
  • betalike
    Beta negative log-likelihood
  • betapdf
    Beta probability density function
  • betarnd
    Beta random numbers
  • betastat
    Beta mean and variance
  • binocdf
    Binomial cumulative distribution function
  • binofit
    Binomial probability estimate
  • binoinv
    Binomial inverse cumulative distribution function
  • binolike
    Binomial negative log-likelihood
  • binopdf
    Binomial probability density function
  • binornd
    Binomial random numbers
  • binostat
    Binomial mean and variance
  • chi2cdf
    Chi-square cumulative distribution function
  • chi2inv
    Chi-square inverse cumulative distribution function
  • chi2pdf
    Chi-square probability density function
  • chi2rnd
    Chi-square random numbers
  • chi2stat
    Chi-square mean and variance
  • evcdf
    Extreme value cumulative distribution function
  • evfit
    Extreme value parameter estimates
  • evinv
    Extreme value inverse cumulative distribution function
  • evlike
    Extreme value negative log-likelihood
  • evpdf
    Extreme value probability density function
  • evrnd
    Extreme value random numbers
  • evstat
    Extreme value mean and variance
  • expcdf
    Exponential cumulative distribution function
  • expfit
    Exponential mean estimate
  • expinv
    Exponential inverse cumulative distribution function
  • explike
    Exponential negative log-likelihood
  • exppdf
    Exponential probability density function
  • exprnd
    Exponential random numbers
  • expstat
    Exponential mean and variance
  • fcdf
    F cumulative distribution function
  • finv
    F inverse cumulative distribution function
  • fpdf
    F probability density function
  • frnd
    F random numbers
  • fstat
    F mean and variance
  • gamcdf
    Gamma cumulative distribution function
  • gamfit
    Gamma parameter estimates
  • gaminv
    Gamma inverse cumulative distribution function
  • gamlike
    Gamma negative log-likelihood
  • gampdf
    Gamma probability density function
  • gamrnd
    Gamma random numbers
  • gamstat
    Gamma mean and variance
  • geocdf
    Geometric cumulative distribution function
  • geofit
    Geometric probability estimate
  • geoinv
    Geometric inverse cumulative distribution function
  • geolike
    Geometric negative log-likelihood
  • geopdf
    Geometric probability density function
  • geornd
    Geometric random numbers
  • geostat
    Geometric mean and variance
  • gevcdf
    Generalized extreme value cumulative distribution function
  • gevfit
    Generalized extreme value parameter estimates
  • gevinv
    Generalized extreme value inverse cumulative distribution function
  • gevlike
    Generalized extreme value negative log-likelihood
  • gevpdf
    Generalized extreme value probability density function
  • gevrnd
    Generalized extreme value random numbers
  • gevstat
    Generalized extreme value mean and variance
  • logncdf
    Lognormal cumulative distribution function
  • lognfit
    Lognormal parameter estimates
  • logninv
    Lognormal inverse cumulative distribution function
  • lognlike
    Lognormal negative log-likelihood
  • lognpdf
    Lognormal probability density function
  • lognrnd
    Lognormal random numbers
  • lognstat
    Lognormal mean and variance
  • nbincdf
    Negative binomial cumulative distribution function
  • nbinfit
    Negative binomial parameter estimates
  • nbininv
    Negative binomial inverse cumulative distribution function
  • nbinlike
    Negative binomial negative log-likelihood
  • nbinpdf
    Negative binomial probability density function
  • nbinrnd
    Negative binomial random numbers
  • nbinstat
    Negative binomial mean and variance
  • normcdf
    Normal cumulative distribution function
  • normfit
    Normal mean and standard deviation estimates
  • norminv
    Normal inverse cumulative distribution function
  • normlike
    Normal negative log-likelihood
  • normpdf
    Normal probability density function
  • normrnd
    Normal random numbers
  • normstat
    Normal mean and variance
  • poisscdf
    Poisson cumulative distribution function
  • poissfit
    Poisson rate estimate
  • poissinv
    Poisson inverse cumulative distribution function
  • poisslike
    Poisson negative log-likelihood
  • poisspdf
    Poisson probability density function
  • poissrnd
    Poisson random numbers
  • poissstat
    Poisson mean and variance
  • randsample
    Random sample from a population.
  • raylcdf
    Rayleigh cumulative distribution function
  • raylfit
    Rayleigh scale estimate
  • raylinv
    Rayleigh inverse cumulative distribution function
  • rayllike
    Rayleigh negative log-likelihood
  • raylpdf
    Rayleigh probability density function
  • raylrnd
    Rayleigh random numbers
  • raylstat
    Rayleigh mean and variance
  • tcdf
    Student t cumulative distribution function
  • tinv
    Student t inverse cumulative distribution function
  • tpdf
    Student t probability density function
  • trnd
    Student t random numbers
  • tstat
    Student t mean and variance
  • unidcdf
    Discrete uniform cumulative distribution function
  • unidfit
    Discrete uniform maximum estimate
  • unidinv
    Discrete uniform inverse cumulative distribution function
  • unidlike
    Discrete uniform negative log-likelihood
  • unidpdf
    Discrete uniform probability density function
  • unidrnd
    Discrete uniform random numbers
  • unidstat
    Discrete uniform mean and variance
  • unifcdf
    Continuous uniform cumulative distribution function
  • unifinv
    Continuous uniform inverse cumulative distribution function
  • unifit
    Continuous uniform parameter estimates
  • uniflike
    Continuous uniform negative log-likelihood
  • unifpdf
    Continuous uniform probability density function
  • unifrnd
    Continuous uniform random numbers
  • unifstat
    Continuous uniform mean and variance
  • wblcdf
    Weibull cumulative distribution function
  • wblfit
    Weibull parameter estimates
  • wblinv
    Weibull inverse cumulative distribution function
  • wbllike
    Weibull negative log-likelihood
  • wblpdf
    Weibull probability density function
  • wblrnd
    Weibull random numbers
  • wblstat
    Weibull mean and variance
Hypothesis Tests

Statistical tests for distribution fit, location, variance, ranks, independence, and comparisons.

  • adtest
    Anderson-Darling goodness-of-fit test.
  • ansaribradley
    Ansari-Bradley test for equal dispersion.
  • chi2gof
    Chi-square goodness-of-fit test.
  • fishertest
    Fisher exact test for a 2-by-2 table.
  • friedman
    Friedman test for blocked data.
  • fsrftest
    Rank predictors using univariate regression F-tests.
  • jbtest
    Jarque-Bera normality test.
  • kruskalwallis
    Kruskal-Wallis one-way analysis of variance by ranks.
  • kstest
    One-sample Kolmogorov-Smirnov test
  • kstest2
    Two-sample Kolmogorov-Smirnov test
  • lillietest
    Lilliefors goodness-of-fit test.
  • ranksum
    Wilcoxon rank sum test.
  • runstest
    Runs test for randomness.
  • signrank
    Wilcoxon signed rank test.
  • signtest
    Sign test.
  • ttest
    One-sample and paired t-test
  • ttest2
    Two-sample t-test
  • vartest
    Chi-square test for a variance
  • vartest2
    F-test for equal variances
  • ztest
    Z-test for a mean with known standard deviation
ANOVA

Analysis of variance functions.

  • anova1
    One-way analysis of variance.
  • anova2
    Two-way analysis of variance.
Regression

Regression, correlation, and supervised prediction functions.

Classification

Classification model functions and helpers for grouped data.

Clustering and Anomaly Detection

Unsupervised learning, nearest-neighbor search, outlier handling, and sequence model functions.

  • cluster
    Construct clusters from a hierarchical cluster tree.
  • clusterdata
    Cluster observations from data.
  • dbscan
    Density-based spatial clustering.
  • dendrogram
    Dendrogram plot for a hierarchical cluster tree.
  • evalclusters
    Evaluate clustering solutions.
  • filloutliers
    Detect and replace outliers in numeric data.
  • fitgmdist
    Fit a Gaussian mixture distribution.
  • gmdistribution
    Gaussian mixture distribution.
  • grpstats
    Summary statistics organized by group.
  • hmmdecode
    Posterior state probabilities for a discrete hidden Markov model.
  • hmmestimate
    Estimate discrete hidden Markov probabilities from known states.
  • hmmgenerate
    Generate a discrete hidden Markov sequence.
  • hmmtrain
    Train a discrete hidden Markov model.
  • hmmviterbi
    Most likely state path for a discrete hidden Markov model.
  • isoutlier
    Find outliers in numeric data.
  • kmeans
    k-means clustering.
  • kmedoids
    Partition data into clusters using medoids.
  • knnsearch
    Find k-nearest neighbors.
  • linkage
    Agglomerative hierarchical cluster tree.
  • mahal
    Squared Mahalanobis distance to reference samples.
  • pdist
    Pairwise distances between observations.
  • pdist2
    Pairwise distances between two sets of observations.
  • rangesearch
    Find all neighbors within a specified distance.
  • rmoutliers
    Detect and remove outliers from numeric data.
  • silhouette
    Silhouette values for clustered data.
  • spectralcluster
    Spectral clustering.
  • squareform
    Convert between condensed distance vector and square distance matrix.
Dimensionality Reduction and Feature Selection

Functions for dimensionality reduction, factor analysis, feature ranking, and low-rank representations.

  • cmdscale
    Classical multidimensional scaling.
  • factoran
    Factor analysis.
  • mdscale
    Nonclassical multidimensional scaling.
  • nnmf
    Nonnegative matrix factorization.
  • pca
    Principal component analysis of raw data.
  • pcacov
    Principal component analysis on a covariance matrix.
  • pcares
    Residuals from principal component analysis.
  • ppca
    Probabilistic principal component analysis.
  • relieff
    Rank predictor importance using ReliefF.
  • rotatefactors
    Rotate factor loadings.
  • sequentialfs
    Sequential feature selection using a custom criterion.
Design of Experiments

Functions for experimental design and model configuration.

  • candexch
    D-optimal row selection from a candidate set.
  • candgen
    Generate a candidate set for designs.
  • cordexch
    D-optimal design using coordinate-style interface.
  • daugment
    Augment a D-optimal design.
  • rowexch
    D-optimal design using row exchange.
  • statget
    Access field values in statistics options structures.
  • statset
    Create or update statistics options structures.
  • x2fx
    Convert factor settings to a design matrix.