MATLAB Arrays

2990 Pages·2011·9.78 MB·English

Statistics Toolbox™
User’s Guide
R2011b
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Revision History
September1993 Firstprinting Version1.0
March1996 Secondprinting Version2.0
January1997 Thirdprinting Version2.11
November2000 Fourthprinting RevisedforVersion3.0(Release12)
May2001 Fifthprinting Minorrevisions
July2002 Sixthprinting RevisedforVersion4.0(Release13)
February2003 Onlineonly RevisedforVersion4.1(Release13.0.1)
June2004 Seventhprinting RevisedforVersion5.0(Release14)
October2004 Onlineonly RevisedforVersion5.0.1(Release14SP1)
March2005 Onlineonly RevisedforVersion5.0.2(Release14SP2)
September2005 Onlineonly RevisedforVersion5.1(Release14SP3)
March2006 Onlineonly RevisedforVersion5.2(Release2006a)
September2006 Onlineonly RevisedforVersion5.3(Release2006b)
March2007 Eighthprinting RevisedforVersion6.0(Release2007a)
September2007 Ninthprinting RevisedforVersion6.1(Release2007b)
March2008 Onlineonly RevisedforVersion6.2(Release2008a)
October2008 Onlineonly RevisedforVersion7.0(Release2008b)
March2009 Onlineonly RevisedforVersion7.1(Release2009a)
September2009 Onlineonly RevisedforVersion7.2(Release2009b)
March2010 Onlineonly RevisedforVersion7.3(Release2010a)
September2010 Onlineonly RevisedforVersion7.4(Release2010b)
April2011 Onlineonly RevisedforVersion7.5(Release2011a)
September2011 Onlineonly RevisedforVersion7.6(Release2011b)

Contents
Getting Started
1
ProductOverview ................................. 1-2
Organizing Data
2
IntroductiontoDataTypes ......................... 2-2
MATLABArrays ................................... 2-4
NumericalData ................................... 2-4
HeterogeneousData ............................... 2-7
StatisticalFunctions ............................... 2-9
StatisticalArrays .................................. 2-11
IntroductiontoStatisticalArrays .................... 2-11
CategoricalArrays ................................ 2-13
DatasetArrays ................................... 2-23
GroupedData ..................................... 2-34
GroupingVariables ................................ 2-34
GroupDefinition .................................. 2-35
FunctionsforGroupedData ......................... 2-35
UsingGroupingVariables .......................... 2-36
Descriptive Statistics
3
IntroductiontoDescriptiveStatistics ............... 3-2
v
MeasuresofCentralTendency ...................... 3-3
MeasuresofDispersion ............................ 3-5
MeasuresofShape ................................. 3-7
ResamplingStatistics .............................. 3-9
TheBootstrap .................................... 3-9
TheJackknife .................................... 3-12
ParallelComputingSupportforResamplingMethods .... 3-13
DatawithMissingValues ........................... 3-14
Statistical Visualization
4
IntroductiontoStatisticalVisualization ............. 4-2
ScatterPlots ...................................... 4-3
BoxPlots ......................................... 4-6
DistributionPlots ................................. 4-8
NormalProbabilityPlots ........................... 4-8
Quantile-QuantilePlots ............................ 4-10
CumulativeDistributionPlots ....................... 4-12
OtherProbabilityPlots ............................. 4-14
Probability Distributions
5
UsingProbabilityDistributions ..................... 5-2
vi Contents
SupportedDistributions ........................... 5-3
ParametricDistributions ........................... 5-4
NonparametricDistributions ........................ 5-8
WorkingwithDistributionsThroughGUIs ........... 5-9
ExploringDistributions ............................ 5-9
ModelingDataUsingtheDistributionFittingTool ...... 5-11
VisuallyExploringRandomNumberGeneration ........ 5-49
StatisticsToolboxDistributionFunctions ........... 5-52
ProbabilityDensityFunctions ....................... 5-52
CumulativeDistributionFunctions ................... 5-62
InverseCumulativeDistributionFunctions ............ 5-66
DistributionStatisticsFunctions ..................... 5-68
DistributionFittingFunctions ....................... 5-70
NegativeLog-LikelihoodFunctions ................... 5-77
RandomNumberGenerators ........................ 5-80
UsingProbabilityDistributionObjects .............. 5-84
UsingDistributionObjects .......................... 5-84
WhatareObjects? ................................. 5-85
CreatingDistributionObjects ....................... 5-88
Object-SupportedDistributions ...................... 5-89
PerformingCalculationsUsingDistributionObjects ..... 5-90
CapturingResultsUsingDistributionObjects .......... 5-97
Probability Distributions Used for Multivariate
Modeling ....................................... 5-99
GaussianMixtureModels ........................... 5-99
Copulas ......................................... 5-107
Random Number Generation
6
GeneratingRandom Data .......................... 6-2
Random NumberGenerationFunctions ............. 6-3
vii
CommonGenerationMethods ...................... 6-5
DirectMethods ................................... 6-5
InversionMethods ................................. 6-7
Acceptance-RejectionMethods ....................... 6-9
Representing Sampling Distributions Using Markov
ChainSamplers ................................. 6-13
UsingtheMetropolis-HastingsAlgorithm .............. 6-13
UsingSliceSampling .............................. 6-14
GeneratingQuasi-RandomNumbers ................ 6-15
Quasi-RandomSequences ........................... 6-15
Quasi-RandomPointSets ........................... 6-16
Quasi-RandomStreams ............................ 6-23
Generating Data Using Flexible Families of
Distributions .................................... 6-25
PearsonandJohnsonSystems ....................... 6-25
GeneratingDataUsingthePearsonSystem ............ 6-26
GeneratingDataUsingtheJohnsonSystem ........... 6-28
Hypothesis Tests
7
IntroductiontoHypothesisTests ................... 7-2
HypothesisTestTerminology ....................... 7-3
HypothesisTestAssumptions ....................... 7-5
Example: HypothesisTesting ....................... 7-7
AvailableHypothesisTests ......................... 7-13
viii Contents
Analysis of Variance
8
IntroductiontoAnalysisofVariance ................ 8-2
ANOVA ........................................... 8-3
One-WayANOVA ................................. 8-3
Two-WayANOVA ................................. 8-9
N-WayANOVA ................................... 8-12
OtherANOVAModels .............................. 8-26
AnalysisofCovariance ............................. 8-27
NonparametricMethods ............................ 8-35
MANOVA ......................................... 8-39
IntroductiontoMANOVA ........................... 8-39
ANOVAwithMultipleResponses .................... 8-39
Parametric Regression Analysis
9
IntroductiontoParametricRegressionAnalysis ..... 9-2
LinearRegression ................................. 9-3
LinearRegressionModels ........................... 9-3
MultipleLinearRegression ......................... 9-8
RobustRegression ................................. 9-14
StepwiseRegression ............................... 9-19
RidgeRegression .................................. 9-29
LassoandElasticNet .............................. 9-32
PartialLeastSquares .............................. 9-46
PolynomialModels ................................ 9-51
ResponseSurfaceModels ........................... 9-59
GeneralizedLinearModels .......................... 9-66
MultivariateRegression ............................ 9-71
NonlinearRegression .............................. 9-72
NonlinearRegressionModels ........................ 9-72
ParametricModels ................................ 9-73
ix
Mixed-EffectsModels .............................. 9-78
Multivariate Methods
10
IntroductiontoMultivariateMethods ............... 10-2
MultidimensionalScaling .......................... 10-3
IntroductiontoMultidimensionalScaling .............. 10-3
ClassicalMultidimensionalScaling ................... 10-3
NonclassicalMultidimensionalScaling ................ 10-8
NonmetricMultidimensionalScaling ................. 10-10
ProcrustesAnalysis ................................ 10-14
ComparingLandmarkData ......................... 10-14
DataInput ....................................... 10-14
PreprocessingDataforAccurateResults .............. 10-15
Example: ComparingHandwrittenShapes ............. 10-16
FeatureSelection .................................. 10-23
IntroductiontoFeatureSelection .................... 10-23
SequentialFeatureSelection ........................ 10-23
FeatureTransformation ............................ 10-28
IntroductiontoFeatureTransformation ............... 10-28
NonnegativeMatrixFactorization .................... 10-28
PrincipalComponentAnalysis(PCA) ................. 10-31
FactorAnalysis ................................... 10-45
Cluster Analysis
11
IntroductiontoClusterAnalysis .................... 11-2
HierarchicalClustering ............................ 11-3
x Contents