11/28/2006

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.