v1.0可编写可改正%Statistics Toolbox%betafit - Beta parameter estimation.%binofit - Binomial parameter estimation.%dfittool - Distribution fitting tool.%evfit - Extreme value parameter estimation.%expfit - Exponential parameter estimation.%gamfit - Gamma parameter estimation.%lognfit - Lognormal parameter estimation.%mle - Maximum likelihood estimation (MLE).%mlecov - Asymptotic covariance matrix of MLE.%nbinfit - Negative binomial parameter estimation.%normfit - Normal parameter estimation.%poissfit - Poisson parameter estimation.%raylfit - Rayleigh parameter estimation.%unifit - Uniform parameter estimation.%wblfit - Weibull parameter estimation.%%Probability density functions (pdf).%betapdf - Beta density.%binopdf - Binomial density.%chi2pdf - Chi square density.%evpdf - Extreme value density.%exppdf - Exponential density.%fpdf - F density.%gampdf - Gamma density.%geopdf - Geometric density.%hygepdf - Hypergeometric density.%lognpdf - Lognormal density.%mvnpdf - Multivariate normal density.%nbinpdf - Negative binomial density.%ncfpdf - Noncentral F density.%nctpdf - Noncentral t density.%ncx2pdf - Noncentral Chi-square density.%normpdf - Normal (Gaussian) density.%pdf - Density function for a specified distribution.%poisspdf - Poisson density.%raylpdf - Rayleigh density.%tpdf - T density.%unidpdf - Discrete uniform density.%unifpdf - Uniform density.%wblpdf - Weibull density.%%Cumulative Distribution functions (cdf).%betacdf - Beta cdf.%binocdf - Binomial cdf.%cdf - Specified cumulative distribution function.%chi2cdf - Chi square cdf.%ecdf - Empirical cdf (Kaplan-Meier estimate).%evcdf - Extreme value cumulative distribution function. %expcdf - Exponential cdf.%fcdf - F cdf.%gamcdf - Gamma cdf.%geocdf - Geometric cdf.%hygecdf - Hypergeometric cdf.%logncdf - Lognormal cdf.%nbincdf - Negative binomial cdf.%ncfcdf - Noncentral F cdf.%nctcdf - Noncentral t cdf.%ncx2cdf - Noncentral Chi-square cdf.%normcdf - Normal (Gaussian) cdf.%poisscdf - Poisson cdf.%raylcdf - Rayleigh cdf.%tcdf - T cdf.%unidcdf - Discrete uniform cdf.%unifcdf - Uniform cdf.%wblcdf - Weibull cdf.%%Critical Values of Distribution functions.%betainv - Beta inverse cumulative distribution function.%binoinv - Binomial inverse cumulative distribution function.%chi2inv - Chi square inverse cumulative distribution function.%evinv - Extreme value inverse cumulative distribution function.%expinv - Exponential inverse cumulative distribution function.%finv - F inverse cumulative distribution function.%gaminv - Gamma inverse cumulative distribution function.%geoinv - Geometric inverse cumulative distribution function.%hygeinv - Hypergeometric inverse cumulative distribution function. %icdf - Specified inverse cdf.%logninv - Lognormal inverse cumulative distribution function.%nbininv - Negative binomial inverse distribution function.%ncfinv - Noncentral F inverse cumulative distribution function.%nctinv - Noncentral t inverse cumulative distribution function.%ncx2inv - Noncentral Chi-square inverse distribution function.%norminv - Normal (Gaussian) inverse cumulative distribution function. %poissinv - Poisson inverse cumulative distribution function.%raylinv - Rayleigh inverse cumulative distribution function.%tinv - T inverse cumulative distribution function.%unidinv - Discrete uniform inverse cumulative distribution function.%unifinv - Uniform inverse cumulative distribution function.%wblinv - Weibull inverse cumulative distribution function.%%Random Number Generators.%betarnd - Beta random numbers.%binornd - Binomial random numbers.%chi2rnd - Chi square random numbers.%evrnd - Extreme value random numbers.%exprnd - Exponential random numbers.%frnd - F random numbers.%gamrnd - Gamma random numbers.%geornd - Geometric random numbers.%hygernd - Hypergeometric random numbers.%iwishrnd - Inverse Wishart random matrix.%lognrnd - Lognormal random numbers.%mvnrnd - Multivariate normal random numbers.%mvtrnd - Multivariate t random numbers.%nbinrnd - Negative binomial random numbers.%ncfrnd - Noncentral F random numbers.%nctrnd - Noncentral t random numbers.%normrnd - Normal (Gaussian) random numbers.%poissrnd - Poisson random numbers.%randg - Gamma random numbers (unit scale).%random - Random numbers from specified distribution. %randsample - Random sample from finite population. %raylrnd - Rayleigh random numbers.%trnd - T random numbers.%unidrnd - Discrete uniform random numbers.%unifrnd - Uniform random numbers.%wblrnd - Weibull random numbers.%wishrnd - Wishart random matrix.%%Statistics.%betastat - Beta mean and variance.%binostat - Binomial mean and variance.%chi2stat - Chi square mean and variance.%evstat - Extreme value mean and variance.%expstat - Exponential mean and variance.%fstat - F mean and variance.%gamstat - Gamma mean and variance.%geostat - Geometric mean and variance.%hygestat - Hypergeometric mean and variance.%lognstat - Lognormal mean and variance.%nbinstat - Negative binomial mean and variance.%ncfstat - Noncentral F mean and variance.%nctstat - Noncentral t mean and variance.%normstat - Normal (Gaussian) mean and variance.%poisstat - Poisson mean and variance.%raylstat - Rayleigh mean and variance.%tstat - T mean and variance.%unidstat - Discrete uniform mean and variance.%unifstat - Uniform mean and variance.%wblstat - Weibull mean and variance.%%Likelihood functions.%betalike - Negative beta log-likelihood.%evlike - Negative extreme value log-likelihood.%explike - Negative exponential log-likelihood.%gamlike - Negative gamma log-likelihood.%lognlike - Negative lognormal log-likelihood.%nbinlike - Negative likelihood for negative binomial distribution. %normlike - Negative normal likelihood.%wbllike - Negative Weibull log-likelihood.%%Descriptive Statistics.%bootstrp - Bootstrap statistics for any function.%corr - Linear or rank correlation coefficient.%corrcoef - Linear correlation coefficient with confidence intervals. %cov - Covariance.%crosstab - Cross tabulation.%geomean - Geometric mean.%grpstats - Summary statistics by group.%harmmean - Harmonic mean.%iqr - Interquartile range.%kurtosis - Kurtosis.%mad - Median Absolute Deviation.%mean - Sample average (in MATLAB toolbox).%median - 50th percentile of a sample.%moment - Moments of a sample.%nanmax - Maximum ignoring NaNs.%nanmean - Mean ignoring NaNs.%nanmedian - Median ignoring NaNs.%nanmin - Minimum ignoring NaNs.%nanstd - Standard deviation ignoring NaNs.%nansum - Sum ignoring NaNs.%nanvar - Variance ignoring NaNs.%prctile - Percentiles.%quantile - Quantiles.%range - Range.%skewness - Skewness.%std - Standard deviation (in MATLAB toolbox).%tabulate - Frequency table.%trimmean - Trimmed mean.%var - Variance (in MATLAB toolbox).%%Linear Models.%addedvarplot - Created added-variable plot for stepwise regression. %anova1 - One-way analysis of variance.%anova2 - Two-way analysis of variance.%anovan - n-way analysis of variance.%aoctool - Interactive tool for analysis of covariance.%dummyvar - Dummy-variable coding.%friedman - Friedman's test (nonparametric two-way anova).%glmfit - Generalized linear model fitting.%glmval - Evaluate fitted values for generalized linear model.%kruskalwallis - Kruskal-Wallis test (nonparametric one-way anova). %leverage - Regression diagnostic.%lscov - Least-squares estimates with known covariance matrix.%lsqnonneg - Non-negative least-squares.%manova1 - One-way multivariate analysis of variance.%manovacluster - Draw clusters of group means for manova1.%multcompare - Multiple comparisons of means and other estimates. %polyconf - Polynomial evaluation and confidence interval estimation. %polyfit - Least-squares polynomial fitting.%polyval - Predicted values for polynomial functions.%rcoplot - Residuals case order plot.%regress - Multivariate linear regression.%regstats - Regression diagnostics.%ridge - Ridge regression.%robustfit - Robust regression model fitting.%rstool - Multidimensional response surface visualization (RSM).%stepwise - Interactive tool for stepwise regression.%stepwisefit - Non-interactive stepwise regression.%x2fx - Factor settings matrix (x) to design matrix (fx).%%Nonlinear Models.%nlinfit - Nonlinear least-squares data fitting.%nlintool - Interactive graphical tool for prediction in nonlinear models.%nlpredci - Confidence intervals for prediction.%nlparci - Confidence intervals for parameters.%%Design of Experiments (DOE).%bbdesign - Box-Behnken design.%candexch - D-optimal design (row exchange algorithm for candidate set). %candgen - Candidates set for D-optimal design generation.%ccdesign - Central composite design.%cordexch - D-optimal design (coordinate exchange algorithm).%daugment - Augment D-optimal design.%dcovary - D-optimal design with fixed covariates.%ff2n - Two-level full-factorial design.%fracfact - Two-level fractional factorial design.%fullfact - Mixed-level full-factorial design.%hadamard - Hadamard matrices (orthogonal arrays).%lhsdesign - Latin hypercube sampling design.%lhsnorm - Latin hypercube multivariate normal sample.%rowexch - D-optimal design (row exchange algorithm).%%Statistical Process Control (SPC).%capable - Capability indices.%capaplot - Capability plot.%ewmaplot - Exponentially weighted moving average plot.%histfit - Histogram with superimposed normal density.%normspec - Plot normal density between specification limits.%schart - S chart for monitoring variability.%xbarplot - Xbar chart for monitoring the mean.%%Multivariate Statistics.%Cluster Analysis.%cophenet - Cophenetic coefficient.%cluster - Construct clusters from LINKAGE output.%clusterdata - Construct clusters from data.%dendrogram - Generate dendrogram plot.%inconsistent - Inconsistent values of a cluster tree.%kmeans - k-means clustering.%linkage - Hierarchical cluster information.%pdist - Pairwise distance between observations.%silhouette - Silhouette plot of clustered data.%squareform - Square matrix formatted distance.%%Dimension Reduction Techniques.%factoran - Factor analysis.%pcacov - Principal components from covariance matrix.%pcares - Residuals from principal components.%princomp - Principal components analysis from raw data.%rotatefactors - Rotation of FA or PCA loadings.%%Plotting.%andrewsplot - Andrews plot for multivariate data.%biplot - Biplot of variable/factor coefficients and scores.%glyphplot - Plot stars or Chernoff faces for multivariate data.%gplotmatrix - Matrix of scatter plots grouped by a common variable. %parallelcoords - Parallel coordinates plot for multivariate data.%%Other Multivariate Methods.%barttest - Bartlett's test for dimensionality.%canoncorr - Cannonical correlation analysis.%cmdscale - Classical multidimensional scaling.%classify - Linear discriminant analysis.%mahal - Mahalanobis distance.%manova1 - One-way multivariate analysis of variance.%mdscale - Metric and non-metric multidimensional scaling.%procrustes - Procrustes analysis.%%Decision Tree Techniques.%treedisp - Display decision tree.%treefit - Fit data using a classification or regression tree.%treeprune - Prune decision tree or creating optimal pruning sequence. %treetest - Estimate error for decision tree.%treeval - Compute fitted values using decision tree.%%Hypothesis Tests.%ranksum - Wilcoxon rank sum test (independent samples).%signrank - Wilcoxon sign rank test (paired samples).%signtest - Sign test (paired samples).%ztest - Z test.%ttest - One sample t test.%ttest2 - Two sample t test.%%Distribution Testing.%jbtest - Jarque-Bera test of normality%kstest - Kolmogorov-Smirnov test for one sample%kstest2 - Kolmogorov-Smirnov test for two samples%lillietest - Lilliefors test of normality%%Nonparametric Functions.%friedman - Friedman's test (nonparametric two-way anova).%kruskalwallis - Kruskal-Wallis test (nonparametric one-way anova).%ksdensity - Kernel smoothing density estimation.%ranksum - Wilcoxon rank sum test (independent samples).%signrank - Wilcoxon sign rank test (paired samples).%signtest - Sign test (paired samples).%%Hidden Markov Models.%hmmdecode - Calculate HMM posterior state probabilities.%hmmestimate - Estimate HMM parameters given state information.%hmmgenerate - Generate random sequence for HMM.%hmmtrain - Calculate maximum likelihood estimates for HMM parameters. %hmmviterbi - Calculate most probable state path for HMM sequence.%%Statistical Plotting.%andrewsplot - Andrews plot for multivariate data.%biplot - Biplot of variable/factor coefficients and scores.%boxplot - Boxplots of a data matrix (one per column).%cdfplot - Plot of empirical cumulative distribution function.%ecdfhist - Histogram calculated from empirical cdf.%fsurfht - Interactive contour plot of a function.%gline - Point, drag and click line drawing on figures.%glyphplot - Plot stars or Chernoff faces for multivariate data.%gname - Interactive point labeling in x-y plots.%gplotmatrix - Matrix of scatter plots grouped by a common variable.%gscatter - Scatter plot of two variables grouped by a third.%hist - Histogram (in MATLAB toolbox).%hist3 - Three-dimensional histogram of bivariate data.%lsline - Add least-square fit line to scatter plot.%normplot - Normal probability plot.%parallelcoords - Parallel coordinates plot for multivariate data.%probplot - Probability plot.%qqplot - Quantile-Quantile plot.%refcurve - Reference polynomial curve.%refline - Reference line.%surfht - Interactive contour plot of a data grid.%wblplot - Weibull probability plot.%%Statistics Demos.%aoctool - Interactive tool for analysis of covariance.%disttool - GUI tool for exploring probability distribution functions.%polytool - Interactive graph for prediction of fitted polynomials.%randtool - GUI tool for generating random numbers.%rsmdemo - Reaction simulation (DOE, RSM, nonlinear curve fitting).%robustdemo - Interactive tool to compare robust and least squares fits. %%File Based I/O.%tblread - Read in data in tabular format.%tblwrite - Write out data in tabular format to file.%tdfread - Read in text and numeric data from tab-delimitted file.%caseread - Read in case names.%casewrite - Write out case names to file.%%Utility Functions.%combnk - Enumeration of all combinations of n objects k at a time. %grp2idx - Convert grouping variable to indices and array of names. %hougen - Prediction function for Hougen model (nonlinear example). %statget - Get STATS options parameter value.%statset - Set STATS options parameter value.%tiedrank - Compute ranks of sample, adjusting for ties.%zscore - Normalize matrix columns to mean 0, variance 1.%Other Utility Functions.%betalik1 - Computation function for negative beta log-likelihood.%boxutil - Utility function for boxplot.%cdfcalc - Computation function for empirical cdf.%dfgetset - Getting and setting dfittool parameters.%dfswitchyard - Invoking private functions for dfittool.%distchck - Argument checking for cdf, pdf and inverse functions.%export2wsdlg - Dialog to export data from gui to workspace.%iscatter - Grouped scatter plot using integer grouping.%meansgraph - Interactive means graph for multiple comparisons.%statdisptable - Display table of statistics.%%HTML Demo Functions.%classdemo - Classification demo.%clusterdemo - Cluster analysis demo.%cmdscaledemo - Classical multidimensional scaling demo.%copulademo - Copula simulation demo.%customdist1demo - Custom distribution fitting demo.%customdist2demo - Custom distribution fitting demo.%factorandemo - Factor analysis demo.%glmdemo - Generalized linear model demo.%gparetodemo - Generalized Pareto fitting demo.%mdscaledemo - Non-classical multidimensional scaling demo. %mvplotdemo - Multidimensional data plotting demo.%samplesizedemo - Sample size calculation demo.%survivaldemo - Survival data analysis demo.%%Obsolete Functions%weibcdf - Weibull cdf, old parameter definitions.%weibfit - Weibull fitting, old parameter definitions.%weibinv - Weibull inv cdf, old parameter definitions.%weiblike - Weibull likelihood, old parameter definitions.%weibpdf - Weibull pdf, old parameter definitions.%weibplot - Weibull prob plot, old parameter definitions.%weibrnd - Weibull random numbers, old parameter definitions. %weibstat - Weibull statistics, old parameter definitions.。
Matlab中的异常值检测算法解析在数据分析和机器学习领域，异常值检测是一个重要的任务，它能够帮助我们发现数据中的异常点或者离群点。
在Matlab中，有许多常用的异常值检测算法可以使用，本文将对其中一些算法进行解析。
1. 异常值检测简介异常值（outliers）是指在大部分数据中与其它观测值显著不同的值。
在许多情况下，异常值可能是由于测量误差、录入错误或者样本本身的特殊性导致的。
异常值的存在可能会对数据分析和建模产生负面影响，因此需要进行异常值检测。
2. Z-Score算法Z-Score算法是一种基于统计的异常值检测方法。
它通过计算数据点与其均值的偏差来判断数据是否异常。
具体而言，Z-Score算法将数据点的值减去均值，再除以标准差，得到的结果就是该数据点的Z-Score值。
如果Z-Score值超过了一个给定的阈值（通常是2或3），则将该数据点标记为异常值。
Z-Score算法的优点是简单易懂，计算速度快。
但是它对数据的分布假设较强，只适用于近似正态分布的数据。
3. 孤立森林算法孤立森林算法是一种基于集成学习的异常值检测方法。
它利用随机生成的决策树对数据进行拆分，然后通过计算样本点到根节点的路径长度来度量样本的异常程度。
孤立森林认为异常点在拆分过程中所需的路径长度会较短，而正常点则需要较长的路径长度。
因此，路径长度越短的样本点越有可能是异常点。
孤立森林算法的优点是可以处理高维数据和大规模数据集，并且对数据的分布假设较弱。
然而，孤立森林算法在处理少量异常点时可能会出现一定的误判。
4. LOF算法LOF（Local Outlier Factor）算法是一种基于邻近度的异常值检测方法。
它通过计算数据点与其邻居之间的密度来判断数据是否异常。
具体而言，LOF算法将一个数据点的邻居分为核心点、边界点和噪声点，然后通过计算一个数据点相对于其邻居的密度比来确定其异常程度。
密度比越大，说明该数据点相对于其邻居的密度越小，即越有可能是异常值。
用mle()函数估计随机数分布的参数$Matlab入门课程, 数学计算Jul 202011MLE(maximum likelihood estimation，最大似然估计)，的基本原理是通过选择参数使似然函数最大化。
此处，我们只讲随机数分布估计。
假设随机分布的PDF为f(x,theta), 其中x为随机数，theta是分布的参数。
我们有x1,x2,…,xn共n个取样观察值，似然函数L(theta)=f(x1,theta)*f(x2,theta)*…*f(xn,theta)然后选择能让L()最大的theta取值。
注意，这个不叫做”极大似然估计”，因为theta可能是有上限或下限，而能够让L()最大的theta值可能恰好是上限或下限，此时的theta就不是极大值点。
下面我们用随机生成的数据实地讲述mle()函数的用法。
语法一：mle(观察值, ‘distribution’, ‘分布名称’), 下面两个命令，第一个是生成100万个服从标准正太分布的随机数，第二句是用mle()函数估计这些随机数服从的正太分布的参数值。
可以获得两个结果，paramhat和paramint，paramhat中有两个数值，第一个是正态分布均值（mu）的点估计，后一个是正态分布的标准差（sigma）。
paramint中第1，2两列分布对应mu和sigma的区间估计。
从结果来看，mu和sigma的区间估计都很窄，而且很接近我们生成随机数时使用的参数值。
这个语法支持的分布类型列表如下（Matlab2011A):‘beta’ Beta‘bernoulli’ Bernoulli‘binomial’ Bino mial‘birnbaumsaunders’ Birnbaum-Saunders‘discrete uniform’ or ‘unid’ Discrete uniform‘exponential’ Exponential‘extreme value’ or ‘ev’ Extreme value‘gamma’ Gamma‘generalized extreme value’ ‘gev’ Generalized extreme value‘generalized pareto’ or‘gp’ Generalized Pareto‘geometric’ Geometric‘inversegaussian’ Inverse Gaussian‘logistic’ Logistic‘loglogistic’ Log-logistic‘lognormal’ Lognormal‘nakagami’ Nakagami‘negative binomial’ or ‘nbin’ Negative binomial‘normal’ Normal‘poisson’ Po isson‘rayleigh’ Rayleigh‘rician’ Rician‘tlocationscale’ t location-scale‘uniform’ Uniform‘weibull’ or ‘wbl’ Weibull语法二：mle(观察值, ‘pdf’, 自定义分布pdf, ‘start’, 猜测的分布参数值), pdf是分布的概率密度函数，格式是f(X,theta)，前面是X，后面跟参数值。
Distributions.Parameter estimation.betafit - Beta parameter estimation.binofit - Binomial parameter estimation.dfittool - Distribution fitting tool.evfit - Extreme value parameter estimation.expfit - Exponential parameter estimation.fitdist - Distribution fitting.gamfit - Gamma parameter estimation.gevfit - Generalized extreme value parameter estimation.gmdistribution - Gaussian mixture model estimation.gpfit - Generalized Pareto parameter estimation.lognfit - Lognormal parameter estimation.mle - Maximum likelihood estimation (MLE).mlecov - Asymptotic covariance matrix of MLE.nbinfit - Negative binomial parameter estimation.normfit - Normal parameter estimation.paretotails - Empirical cdf with generalized Pareto tails.poissfit - Poisson parameter estimation.raylfit - Rayleigh parameter estimation.unifit - Uniform parameter estimation.wblfit - Weibull parameter estimation. Probability density functions (pdf).betapdf - Beta density.binopdf - Binomial density.chi2pdf - Chi square density.evpdf - Extreme value density.exppdf - Exponential density.fpdf - F density.gampdf - Gamma density.geopdf - Geometric density.gevpdf - Generalized extreme value density. gppdf - Generalized Pareto density.hygepdf - Hypergeometric density.lognpdf - Lognormal density.mnpdf - Multinomial probability density function. mvnpdf - Multivariate normal density.mvtpdf - Multivariate t density.nbinpdf - Negative binomial density.ncfpdf - Noncentral F density.nctpdf - Noncentral t density.ncx2pdf - Noncentral Chi-square density. normpdf - Normal (Gaussian) density.pdf - Density function for a specified distribution.poisspdf - Poisson density.raylpdf - Rayleigh density.tpdf - T density.unidpdf - Discrete uniform density.unifpdf - Uniform density.wblpdf - Weibull density.Cumulative Distribution functions (cdf).betacdf - Beta cumulative distribution function.binocdf - Binomial cumulative distribution function.cdf - Specified cumulative distribution function.chi2cdf - Chi square cumulative distribution function.ecdf - Empirical cumulative distribution function (Kaplan-Meier estimate).evcdf - Extreme value cumulative distribution function.expcdf - Exponential cumulative distribution function.fcdf - F cumulative distribution function.gamcdf - Gamma cumulative distribution function.geocdf - Geometric cumulative distribution function.gevcdf - Generalized extreme value cumulative distribution function.gpcdf - Generalized Pareto cumulative distribution function.hygecdf - Hypergeometric cumulative distribution function.logncdf - Lognormal cumulative distribution function.mvncdf - Multivariate normal cumulative distribution function. mvtcdf - Multivariate t cumulative distribution function. nbincdf - Negative binomial cumulative distribution function. ncfcdf - Noncentral F cumulative distribution function.nctcdf - Noncentral t cumulative distribution function.ncx2cdf - Noncentral Chi-square cumulative distribution function. normcdf - Normal (Gaussian) cumulative distribution function. poisscdf - Poisson cumulative distribution function.raylcdf - Rayleigh cumulative distribution function.tcdf - T cumulative distribution function.unidcdf - Discrete uniform cumulative distribution function. unifcdf - Uniform cumulative distribution function.wblcdf - Weibull cumulative distribution function.Critical Values of Distribution functions.betainv - Beta inverse cumulative distribution function.binoinv - Binomial inverse cumulative distribution function.chi2inv - Chi square inverse cumulative distribution function. evinv - Extreme value inverse cumulative distribution function. expinv - Exponential inverse cumulative distribution function. finv - F inverse cumulative distribution function.gaminv - Gamma inverse cumulative distribution function.geoinv - Geometric inverse cumulative distribution function.gevinv - Generalized extreme value inverse cumulative distribution function.gpinv - Generalized Pareto inverse cumulative distribution function.hygeinv - Hypergeometric inverse cumulative distribution function.icdf - Specified inverse cumulative distribution function.logninv - Lognormal inverse cumulative distribution function.nbininv - Negative binomial inverse distribution function.ncfinv - Noncentral F inverse cumulative distribution function.nctinv - Noncentral t inverse cumulative distribution function.ncx2inv - Noncentral Chi-square inverse distribution function.norminv - Normal (Gaussian) inverse cumulative distribution function.poissinv - Poisson inverse cumulative distribution function.raylinv - Rayleigh inverse cumulative distribution function.tinv - T inverse cumulative distribution function.unidinv - Discrete uniform inverse cumulative distribution function.unifinv - Uniform inverse cumulative distribution function.wblinv - Weibull inverse cumulative distribution function.Random Number Generators.betarnd - Beta random numbers.binornd - Binomial random numbers.chi2rnd - Chi square random numbers.evrnd - Extreme value random numbers.exprnd - Exponential random numbers.frnd - F random numbers.gamrnd - Gamma random numbers.geornd - Geometric random numbers.gevrnd - Generalized extreme value random numbers.gprnd - Generalized Pareto inverse random numbers.hygernd - Hypergeometric random numbers.iwishrnd - Inverse Wishart random matrix.johnsrnd - Random numbers from the Johnson system of distributions. lognrnd - Lognormal random numbers.mhsample - Metropolis-Hastings algorithm.mnrnd - Multinomial random vectors.mvnrnd - Multivariate normal random vectors.mvtrnd - Multivariate t random vectors.nbinrnd - Negative binomial random numbers.ncfrnd - Noncentral F random numbers.nctrnd - Noncentral t random numbers.ncx2rnd - Noncentral Chi-square random numbers.normrnd - Normal (Gaussian) random numbers.pearsrnd - Random numbers from the Pearson system of distributions. poissrnd - Poisson random numbers.randg - Gamma random numbers (unit scale). random - Random numbers from specified distribution. randsample - Random sample from finite population. raylrnd - Rayleigh random numbers.slicesample - Slice sampling method.trnd - T random numbers.unidrnd - Discrete uniform random numbers.unifrnd - Uniform random numbers.wblrnd - Weibull random numbers.wishrnd - Wishart random matrix.Quasi-Random Number Generators.haltonset - Halton sequence point set.qrandstream - Quasi-random stream.sobolset - Sobol sequence point set.Statistics.betastat - Beta mean and variance.binostat - Binomial mean and variance.chi2stat - Chi square mean and variance.evstat - Extreme value mean and variance.expstat - Exponential mean and variance.fstat - F mean and variance.gamstat - Gamma mean and variance.geostat - Geometric mean and variance.gevstat - Generalized extreme value mean and variance. gpstat - Generalized Pareto inverse mean and variance. hygestat - Hypergeometric mean and variance. lognstat - Lognormal mean and variance.nbinstat - Negative binomial mean and variance. ncfstat - Noncentral F mean and variance.nctstat - Noncentral t mean and variance.ncx2stat - Noncentral Chi-square mean and variance. normstat - Normal (Gaussian) mean and variance. poisstat - Poisson mean and variance.raylstat - Rayleigh mean and variance.tstat - T mean and variance.unidstat - Discrete uniform mean and variance.unifstat - Uniform mean and variance.wblstat - Weibull mean and variance.Likelihood functions.betalike - Negative beta log-likelihood.evlike - Negative extreme value log-likelihood. explike - Negative exponential log-likelihood. gamlike - Negative gamma log-likelihood.gevlike - Generalized extreme value log-likelihood.gplike - Generalized Pareto inverse log-likelihood. lognlike - Negative lognormal log-likelihood.nbinlike - Negative binomial log-likelihood.normlike - Negative normal likelihood.wbllike - Negative Weibull log-likelihood.Probability distribution objects.ProbDistUnivKernel - Univariate kernel smoothing distributions. ProbDistUnivParam - Univariate parametric distributions. Descriptive Statistics.bootci - Bootstrap confidence intervals.bootstrp - Bootstrap statistics.corr - Linear or rank correlation coefficient.corrcoef - Linear correlation coefficient (in MATLAB toolbox). cov - Covariance (in MATLAB toolbox).crosstab - Cross tabulation.geomean - Geometric mean.grpstats - Summary statistics by group.harmmean - Harmonic mean.iqr - Interquartile range.jackknife - Jackknife statistics.kurtosis - Kurtosis.mad - Median Absolute Deviation.mean - Sample average (in MATLAB toolbox).median - 50th percentile of a sample (in MATLAB toolbox).mode - Mode, or most frequent value in a sample (in MATLAB toolbox). moment - Moments of a sample.nancov - Covariance matrix ignoring NaNs.nanmax - Maximum ignoring NaNs.nanmean - Mean ignoring NaNs.nanmedian - Median ignoring NaNs.nanmin - Minimum ignoring NaNs.nanstd - Standard deviation ignoring NaNs.nansum - Sum ignoring NaNs.nanvar - Variance ignoring NaNs.partialcorr - Linear or rank partial correlation coefficient.prctile - Percentiles.quantile - Quantiles.range - Range.skewness - Skewness.std - Standard deviation (in MATLAB toolbox).tabulate - Frequency table.trimmean - Trimmed mean.var - Variance (in MATLAB toolbox).Linear Models.addedvarplot - Created added-variable plot for stepwise regression.anova1 - One-way analysis of variance.anova2 - Two-way analysis of variance.anovan - n-way analysis of variance.aoctool - Interactive tool for analysis of covariance.dummyvar - Dummy-variable coding.friedman - Friedman's test (nonparametric two-way anova).glmfit - Generalized linear model fitting.glmval - Evaluate fitted values for generalized linear model.invpred - Inverse prediction for simple linear regression.kruskalwallis - Kruskal-Wallis test (nonparametric one-way anova).leverage - Regression diagnostic.lscov - Ordinary, weighted, or generalized least-squares (in MATLAB toolbox).lsqnonneg - Non-negative least-squares (in MATLAB toolbox).manova1 - One-way multivariate analysis of variance.manovacluster - Draw clusters of group means for manova1.mnrfit - Nominal or ordinal multinomial regression model fitting.mnrval - Predict values for nominal or ordinal multinomial regression.multcompare - Multiple comparisons of means and other estimates. mvregress - Multivariate regression with missing data.mvregresslike - Negative log-likelihood for multivariate regression. polyconf - Polynomial evaluation and confidence interval estimation. polyfit - Least-squares polynomial fitting (in MATLAB toolbox).polyval - Predicted values for polynomial functions (in MATLAB toolbox). rcoplot - Residuals case order plot.regress - Multiple linear regression using least squares.regstats - Regression diagnostics.ridge - Ridge regression.robustfit - Robust regression model fitting.rstool - Multidimensional response surface visualization (RSM). stepwise - Interactive tool for stepwise regression.stepwisefit - Non-interactive stepwise regression.x2fx - Factor settings matrix (x) to design matrix (fx).Nonlinear Models.coxphfit - Cox proportional hazards regression.nlinfit - Nonlinear least-squares data fitting.nlintool - Interactive graphical tool for prediction in nonlinear models. nlmefit - Nonlinear mixed-effects data fitting.nlpredci - Confidence intervals for prediction.nlparci - Confidence intervals for parameters.Design of Experiments (DOE).bbdesign - Box-Behnken design.candexch - D-optimal design (row exchange algorithm for candidate set). candgen - Candidates set for D-optimal design generation.ccdesign - Central composite design.cordexch - D-optimal design (coordinate exchange algorithm). daugment - Augment D-optimal design.dcovary - D-optimal design with fixed covariates.fracfactgen - Fractional factorial design generators.ff2n - Two-level full-factorial design.fracfact - Two-level fractional factorial design.fullfact - Mixed-level full-factorial design.hadamard - Hadamard matrices (orthogonal arrays) (in MATLAB toolbox). lhsdesign - Latin hypercube sampling design.lhsnorm - Latin hypercube multivariate normal sample.rowexch - D-optimal design (row exchange algorithm).Statistical Process Control (SPC).capability - Capability indices.capaplot - Capability plot.controlchart - Shewhart control chart.controlrules - Control rules (Western Electric or Nelson) for SPC data.gagerr - Gage repeatability and reproducibility (R&R) study. histfit - Histogram with superimposed normal density. normspec - Plot normal density between specification limits. runstest - Runs test for randomness.Multivariate Statistics.Cluster Analysis.cophenet - Cophenetic coefficient.cluster - Construct clusters from LINKAGE output. clusterdata - Construct clusters from data.dendrogram - Generate dendrogram plot.gmdistribution - Gaussian mixture model estimation. inconsistent - Inconsistent values of a cluster tree.kmeans - k-means clustering.linkage - Hierarchical cluster information.pdist - Pairwise distance between observations. silhouette - Silhouette plot of clustered data.squareform - Square matrix formatted distance. Classification.classify - Linear discriminant analysis.NaiveBayes - Naive Bayes classification.Dimension Reduction T echniques.factoran - Factor analysis.nnmf - Non-negative matrix factorization.pcacov - Principal components from covariance matrix. pcares - Residuals from principal components.princomp - Principal components analysis from raw data. rotatefactors - Rotation of FA or PCA loadings.Copulascopulacdf - Cumulative probability function for a copula. copulafit - Fit a parametric copula to data.copulaparam - Copula parameters as a function of rank correlation. copulapdf - Probability density function for a copula. copularnd - Random vectors from a copula.copulastat - Rank correlation for a copula.Plotting.andrewsplot - Andrews plot for multivariate data.biplot - Biplot of variable/factor coefficients and scores. interactionplot - Interaction plot for factor effects. maineffectsplot - Main effects plot for factor effects.glyphplot - Plot stars or Chernoff faces for multivariate data. gplotmatrix - Matrix of scatter plots grouped by a common variable. multivarichart - Multi-vari chart of factor effects.parallelcoords - Parallel coordinates plot for multivariate data.Other Multivariate Methods.barttest - Bartlett's test for dimensionality.canoncorr - Canonical correlation analysis.cmdscale - Classical multidimensional scaling.mahal - Mahalanobis distance.manova1 - One-way multivariate analysis of variance.mdscale - Metric and non-metric multidimensional scaling. mvregress - Multivariate regression with missing data.plsregress - Partial least squares regression.procrustes - Procrustes analysis.Decision Tree Techniques.classregtree - Classification and regression tree.TreeBagger - Ensemble of bagged decision trees. CompactTreeBagger - Lightweight ensemble of bagged decision trees. Hypothesis Tests.ansaribradley - Ansari-Bradley two-sample test for equal dispersions. dwtest - Durbin-Watson test for autocorrelation in linear regression. linhyptest - Linear hypothesis test on parameter estimates.ranksum - Wilcoxon rank sum test (independent samples). runstest - Runs test for randomness.sampsizepwr - Sample size and power calculation for hypothesis test. signrank - Wilcoxon sign rank test (paired samples).signtest - Sign test (paired samples).ttest - One sample t test.ttest2 - Two sample t test.vartest - One-sample test of variance.vartest2 - Two-sample F test for equal variances.vartestn - Test for equal variances across multiple groups.ztest - Z test.Distribution Testing.chi2gof - Chi-square goodness-of-fit test.jbtest - Jarque-Bera test of normality.kstest - Kolmogorov-Smirnov test for one sample.kstest2 - Kolmogorov-Smirnov test for two samples.lillietest - Lilliefors test of normality.Nonparametric Functions.friedman - Friedman's test (nonparametric two-way anova). kruskalwallis - Kruskal-Wallis test (nonparametric one-way anova). ksdensity - Kernel smoothing density estimation.ranksum - Wilcoxon rank sum test (independent samples). signrank - Wilcoxon sign rank test (paired samples).signtest - Sign test (paired samples).Hidden Markov Models.hmmdecode - Calculate HMM posterior state probabilities.hmmestimate - Estimate HMM parameters given state information.hmmgenerate - Generate random sequence for HMM.hmmtrain - Calculate maximum likelihood estimates for HMM parameters.hmmviterbi - Calculate most probable state path for HMM sequence.Model Assessment.confusionmat - Confusion matrix for classification algorithms.crossval - Loss estimate using cross-validation.cvpartition - Cross-validation partition.perfcurve - ROC and other performance measures for classification algorithms.Model Selection.sequentialfs - Sequential feature selection.stepwise - Interactive tool for stepwise regression.stepwisefit - Non-interactive stepwise regression.Statistical Plotting.andrewsplot - Andrews plot for multivariate data.biplot - Biplot of variable/factor coefficients and scores.boxplot - Boxplots of a data matrix (one per column).cdfplot - Plot of empirical cumulative distribution function. ecdf - Empirical cdf (Kaplan-Meier estimate).ecdfhist - Histogram calculated from empirical cdf.fsurfht - Interactive contour plot of a function.gline - Point, drag and click line drawing on figures. glyphplot - Plot stars or Chernoff faces for multivariate data. gname - Interactive point labeling in x-y plots.gplotmatrix - Matrix of scatter plots grouped by a common variable. gscatter - Scatter plot of two variables grouped by a third.hist - Histogram (in MATLAB toolbox).hist3 - Three-dimensional histogram of bivariate data. ksdensity - Kernel smoothing density estimation.lsline - Add least-square fit line to scatter plot.normplot - Normal probability plot.parallelcoords - Parallel coordinates plot for multivariate data. probplot - Probability plot.qqplot - Quantile-Quantile plot.refcurve - Reference polynomial curve.refline - Reference line.scatterhist - 2D scatter plot with marginal histograms.surfht - Interactive contour plot of a data grid.wblplot - Weibull probability plot.Data Objectsdataset - Create datasets from workspace variables or files. nominal - Create arrays of nominal data.ordinal - Create arrays of ordinal data.Statistics Demos.aoctool - Interactive tool for analysis of covariance.disttool - GUI tool for exploring probability distribution functions. polytool - Interactive graph for prediction of fitted polynomials. randtool - GUI tool for generating random numbers.rsmdemo - Reaction simulation (DOE, RSM, nonlinear curve fitting). robustdemo - Interactive tool to compare robust and least squares fits. File Based I/O.tblread - Read in data in tabular format.tblwrite - Write out data in tabular format to file.tdfread - Read in text and numeric data from tab-delimited file. caseread - Read in case names.casewrite - Write out case names to file.Utility Functions.cholcov - Cholesky-like decomposition for covariance matrix.combnk - Enumeration of all combinations of n objects k at a time. corrcov - Convert covariance matrix to correlation matrix.grp2idx - Convert grouping variable to indices and array of names. hougen - Prediction function for Hougen model (nonlinear example). statget - Get STATS options parameter value.statset - Set STATS options parameter value.tiedrank - Compute ranks of sample, adjusting for ties.zscore - Normalize matrix columns to mean 0, variance 1. Overloaded methods:xregusermod/statsxregunispline/statsxregnnet/statsxregmultilin/statsxregmodel/statsxreglinear/statsxreginterprbf/stats。
