11.3 統計指令一覽表

在大部份之機率分佈計算中，有些指令尚提供參數及信任水準的計算方法。為獲得相關指令，可以使用help stats進行查詢。例如：

>> help stats
  Statistics Toolbox
  Version 5.0 (R14) 05-May-2004
 
  
Distributions.
   Parameter estimation.
    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.
    ncx2rnd     - Noncentral Chi-square 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.
    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.
    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.