IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents a set of data points, where each data point consists of a single real number. More...
Public Member Functions | |
Sample () | |
Initializes a new, empty sample. More... | |
Sample (string name) | |
Initializes a new, empty sample with the given name. More... | |
Sample (IEnumerable< double > values) | |
Initializes a new sample from a list of values. More... | |
Sample (params double[] values) | |
Initializes a new sample from a list of values. More... | |
void | Add (double value) |
Adds a value to the sample. More... | |
void | Add (IEnumerable< double > values) |
Adds multiple values to the sample. More... | |
void | Add (params double[] values) |
Adds multiple values to the sample. More... | |
bool | Remove (double value) |
Removes a given value from the sample. More... | |
void | Clear () |
Remove all values from the sample. More... | |
void | Transform (Func< double, double > transformFunction) |
Transforms all values using a user-supplied function. More... | |
bool | Contains (double value) |
Determines whether the sample contains the given value. More... | |
Sample | Copy () |
Copies the sample. More... | |
double | Moment (int n) |
Computes the given sample moment. More... | |
double | MomentAboutMean (int n) |
Computes the given sample moment about its mean. More... | |
double | LeftProbability (double value) |
Gets the fraction of values equal to or less than the given value. More... | |
double | InverseLeftProbability (double P) |
Gets the sample value corresponding to a given percentile score. More... | |
UncertainValue | PopulationMoment (int n) |
Estimates the given population moment using the sample. More... | |
UncertainValue | PopulationMomentAboutMean (int n) |
Estimates the given population moment about the mean using the sample. More... | |
TestResult | ZTest (double referenceMean, double referenceStandardDeviation) |
Performs a z-test. More... | |
TestResult | StudentTTest (double referenceMean) |
Tests whether the sample mean is compatible with the reference mean. More... | |
TestResult | SignTest (double referenceMedian) |
Tests whether the sample median is compatible with the given reference value. More... | |
TestResult | KolmogorovSmirnovTest (Distribution distribution) |
Tests whether the sample is compatible with the given distribution. More... | |
TestResult | KuiperTest (Distribution distribution) |
Tests whether the sample is compatible with the given distribution. More... | |
IEnumerator< double > | GetEnumerator () |
Gets an enumerator of sample values. More... | |
FitResult | MaximumLikelihoodFit (IParameterizedDistribution distribution) |
Performs a maximum likelihood fit. More... | |
void | Load (IDataReader reader, int dbIndex) |
Loads values from a data reader. More... | |
Static Public Member Functions | |
static TestResult | StudentTTest (Sample a, Sample b) |
Tests whether one sample mean is compatible with another sample mean. More... | |
static TestResult | MannWhitneyTest (Sample a, Sample b) |
Tests whether the sample median is compatible with the mean of another sample. More... | |
static OneWayAnovaResult | OneWayAnovaTest (params Sample[] samples) |
Performs a one-way ANOVA. More... | |
static OneWayAnovaResult | OneWayAnovaTest (IList< Sample > samples) |
Performs a one-way ANOVA. More... | |
static TestResult | KruskalWallisTest (IList< Sample > samples) |
Performs a Kruskal-Wallis test on the given samples. More... | |
static TestResult | KruskalWallisTest (params Sample[] samples) |
Performs a Kruskal-Wallis test on the given samples. More... | |
static TestResult | KolmogorovSmirnovTest (Sample a, Sample b) |
Tests whether the sample is compatible with another sample. More... | |
static TestResult | FisherFTest (Sample a, Sample b) |
Tests whether the variance of two samples is compatible. More... | |
Properties | |
string | Name [get, set] |
Gets or sets the name of the sample. More... | |
bool | IsReadOnly [get] |
Gets a value indicating whether the sample is read-only. More... | |
int | Count [get] |
Gets the number of values in the sample. More... | |
double | Mean [get] |
Gets the sample mean. More... | |
double | Variance [get] |
Gets the sample variance. More... | |
double | StandardDeviation [get] |
Gets the sample standard deviation. More... | |
double | Skewness [get] |
Gets the sample skewness. More... | |
double | Median [get] |
Gets the sample median. More... | |
Interval | InterquartileRange [get] |
Gets the interquartile range of sample measurmements. More... | |
double | Minimum [get] |
Gets the smallest value in the sample. More... | |
double | Maximum [get] |
Gets the largest value in the sample. More... | |
UncertainValue | PopulationMean [get] |
Gets an estimate of the population mean from the sample. More... | |
UncertainValue | PopulationVariance [get] |
Gets an estimate of the population variance from the sample. More... | |
UncertainValue | PopulationStandardDeviation [get] |
Gets an estimate of the population standard deviation from the sample. More... | |
Private Member Functions | |
UncertainValue | EstimateFirstCumulant () |
UncertainValue | EstimateSecondCumulant () |
UncertainValue | EstimateThirdCumulant () |
UncertainValue | EstimateCentralMoment (int r) |
TestResult | KolmogorovSmirnovTest (Distribution distribution, int count) |
void | ComputeDStatistics (Distribution distribution, out double D1, out double D2) |
IEnumerator IEnumerable. | GetEnumerator () |
void ICollection< double >. | CopyTo (double[] array, int start) |
Private Attributes | |
SampleStorage | data |
bool | isReadOnly |
Represents a set of data points, where each data point consists of a single real number.
A univariate sample is a data set which records one number for each independent observation. For example, data from a study which measured the weight of each subject could be stored in the Sample class. The class offers descriptive statistics for the sample, estimates of descriptive statistics of the underlying population distribution, and statistical tests to compare the sample distribution to other sample distributions or theoretical models.
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Initializes a new, empty sample.
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Initializes a new, empty sample with the given name.
name | The name of the sample. |
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Initializes a new sample from a list of values.
values | Values to add to the sample. |
ArgumentNullException | values is null. |
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Initializes a new sample from a list of values.
values | Values to add to the sample. |
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Adds a value to the sample.
value | The value to add. |
Referenced by Test.SampleTest.AnovaDistribution(), Test.SampleTest.AnovaTest(), Test.BivariateSampleTest.BivariateLinearRegression(), Test.BivariateSampleTest.BivariateLinearRegressionGoodnessOfFitDistribution(), Test.MultivariateSampleTest.BivariateNullAssociation(), Test.BivariateSampleTest.BivariatePolynomialRegression(), Test.BugTests.Bug7213(), FutureTest.FutureTest.ChiSquareDistribution(), Test.SampleTest.CreateSample(), Test.SampleTest.ExponentialFitUncertainty(), Test.DistributionTest.FisherTest(), Test.DataSetTest.FitDataToLineChiSquaredTest(), Test.DataSetTest.FitDataToPolynomialChiSquaredTest(), Test.DataSetTest.FitDataToPolynomialUncertaintiesTest(), Test.DistributionTest.GammaFromExponential(), Test.DistributionTest.InverseGaussianSummation(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.SampleTest.LowSampleMoments(), Test.MultivariateSampleTest.MultivariateLinearRegressionNullDistribution(), Test.BivariateSampleTest.PearsonRDistribution(), Test.SampleTest.SampleCopy(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleManipulations(), Test.SampleTest.SampleMedian(), Test.SampleTest.SignTestDistribution(), Test.NullDistributionTests.SpearmanNullDistributionTest(), Test.DistributionTest.StudentTest(), Test.DistributionTest.StudentTest2(), Test.RandomTest.TimeGammaGenerators(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), FutureTest.FutureTest.TwoSampleKS2(), Test.DistributionTest.UniformOrderStatistics(), Test.SampleTest.WaldFitUncertainties(), and Test.SampleTest.ZTestDistribution().
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Adds multiple values to the sample.
values | An enumerable set of the values to add. |
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Adds multiple values to the sample.
values | An arbitrary number of values. |
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Removes a given value from the sample.
value | The value to remove. |
Referenced by Test.SampleTest.LowSampleMoments(), and Test.SampleTest.SampleManipulations().
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Remove all values from the sample.
Referenced by Test.SampleTest.SampleManipulations().
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Transforms all values using a user-supplied function.
transformFunction | The function used to transform the values, which must not be null. |
For example, to replace all values with their logarithms, apply a transform using Math.Log(double).
If the supplied transform function throws an excaption, or returns infinite or NaN values, the transformation may be incomplete or the data corrupted.
Referenced by Test.SampleTest.SampleTransform().
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Determines whether the sample contains the given value.
value | The value to check for. |
Referenced by Test.SampleTest.SampleManipulations().
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Copies the sample.
Referenced by Test.SampleTest.SampleCopy().
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Computes the given sample moment.
n | The order of the moment to compute. |
References Meta.Numerics.MoreMath.Pow(), and Meta.Numerics.MoreMath.Sqr().
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Computes the given sample moment about its mean.
n | The order of the moment to compute. |
References Meta.Numerics.MoreMath.Pow().
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Gets the fraction of values equal to or less than the given value.
value | The reference value. |
Referenced by Test.BugTests.Bug6988().
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Gets the sample value corresponding to a given percentile score.
P | The percentile, which must lie between zero and one. |
ArgumentOutOfRangeException | P lies outside [0,1]. |
InsufficientDataException | Sample.Count is less than two. |
Referenced by Test.BugTests.Bug6988(), Meta.Numerics.Statistics.Distributions.WeibullDistribution.FitToSample(), and Test.SampleTest.SampleInterquartileRange().
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Estimates the given population moment using the sample.
n | The order of the moment. |
Referenced by Test.SampleTest.SampleMoments().
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Estimates the given population moment about the mean using the sample.
n | The order of the moment. |
ArgumentOutOfRangeException | n is negative. |
Referenced by Test.SampleTest.SampleMoments(), Test.SampleTest.SamplePopulationMomentEstimateVariances(), Test.SampleTest.SignTestDistribution(), and Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest().
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Performs a z-test.
referenceMean | The mean of the comparison population. |
referenceStandardDeviation | The standard deviation of the comparison population. |
A z-test determines whether the sample is compatible with a normal population with known mean and standard deviation. In most cases, Student's t-test (StudentTTest(double)), which does not assume a known population standard deviation, is more appropriate.
Suppose a standardized test exists, for which it is known that the mean score is 100 and the standard deviation is 15 across the entire population. The test is administered to a small sample of a subpopulation, who obtain a mean sample score of 95. You can use the z-test to determine how likely it is that the subpopulation mean really is lower than the population mean, that is that their slightly lower mean score in your sample is not merely a fluke.
InsufficientDataException | Sample.Count is zero. |
Referenced by Test.SampleTest.ZTestDistribution().
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Tests whether the sample mean is compatible with the reference mean.
referenceMean | The reference mean. |
The test statistic of Student's t-test is the difference between the sample mean and the reference mean, measured in units of the sample mean uncertainty. Under the null hypothesis that the sample was drawn from a normally distributed population with the given reference mean, this statistic can be shown to follow a Student distribution (StudentDistribution). If t is far from zero, with correspondingly small left or right tail probability, then the sample is unlikely to have been drawn from a population with the given reference mean.
Because the distribution of a t-statistic assumes a normally distributed population, this test should only be used only on sample data compatible with a normal distribution. The sign test (SignTest) is a non-parametric alternative that can be used to test the compatibility of the sample median with an assumed population median.
In some country, the legal limit blood alcohol limit for drivers is 80 on some scale. Because they have noticed that the results given by their measuring device fluctuate, the police perform three seperate measurements on a suspected drunk driver. They obtain the results 81, 84, and 93. They argue that, because all three results exceed the limit, the court should be very confident that the driver's blood alcohol level did, in fact, exceed the legal limit. You are the driver's lawyer. Can you make an argument to that the court shouldn't be so sure?
Here is some code that computes the probability of obtaining such high measured values, assuming that the true level is exactly 80.
What level of statistical confidence do you think should a court require in order to pronounce a defendant guilty?
InsufficientDataException | There are fewer than two data points in the sample. |
Referenced by Test.SampleTest.AnovaStudentAgreement(), and Test.SampleTest.TTestDistribution().
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Tests whether the sample median is compatible with the given reference value.
referenceMedian | The reference median. |
The sign test is a non-parametric alternative to the Student t-test (StudentTTest(double)). It tests whether the sample is consistent with the given refernce median.
The null hypothesis for the test is that the median of the underlying population from which the sample is drawn is the reference median. The test statistic is simply number of sample values that lie above the median. Since each sample value is equally likely to be below or above the population median, each draw is an independent Bernoulli trial, and the total number of values above the population median is distributed accordng to a binomial distribution (BinomialDistribution).
The left probability of the test result is the chance of the sample median being so low, assuming the sample to have been drawn from a population with the reference median. The right probability of the test result is the chance of the sample median being so high, assuming the sample to have been drawn from a population with the reference median.
Referenced by Test.SampleTest.SignTestDistribution().
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Tests whether one sample mean is compatible with another sample mean.
a | The first sample, which must contain at least two entries. |
b | The second sample, which must contain at least two entries. |
References Meta.Numerics.Statistics.Sample.Count, and Meta.Numerics.Statistics.Sample.Mean.
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Tests whether the sample median is compatible with the mean of another sample.
a | The fisrt sample. |
b | The second sample. |
The Mann-Whitney test is a non-parametric alternative to Student's t-test. Essentially, it supposes that the medians of the two samples are equal and tests the likelihood of this null hypothesis. Unlike the t-test, it does not assume that the sample distributions are normal.
References Meta.Numerics.Statistics.Sample.Count, Meta.Numerics.Statistics.Sample.data, and Meta.Numerics.Functions.AdvancedIntegerMath.LogFactorial().
Referenced by Test.SampleTest.SampleMannWhitneyTest().
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Performs a one-way ANOVA.
samples | The samples to compare. |
The one-way ANOVA is an extension of the Student t-test (StudentTTest(Sample,Sample)) to more than two groups. The test's null hypothesis is that all the groups' data are drawn from the same distribution. If the null hypothesis is rejected, it indicates that at least one of the groups differs significantly from the others.
Given more than two groups, you should use an ANOVA to test for differences in the means of the groups rather than perform multiple t-tests. The reason is that each t-test incurs a small risk of a false positive, so multiple t-tests increase the total risk of a false positive. For example, given a 95% confidence requirement, there is only a 5% chance that a t-test will incorrectly diagnose a significant difference. But given 5 samples, there are 5 * 4 /2 = 10 t-tests to be performed, giving about a 40% chance that at least one of them will incorrectly diagnose a significant difference! The ANOVA avoids the accumulation of risk by performing a single test at the required confidence level to test for any significant differences between the groups.
A one-way ANOVA performed on just two samples is equivilent to a t-test (Sample.StudentTTest(Sample,Sample)).
ANOVA is an acronym for "Analysis of Variance". Do not be confused by the name and by the use of a ratio-of-variances test statistic: an ANOVA is primarily (although not exclusively) sensitive to changes in the mean between samples. The variances being compared by the test are not the variances of the individual samples; instead the test is comparing the variance of all samples considered together as one single sample to the variances of the samples considered individually. If the means of some groups differ significantly, then the variance of the unified sample will be much larger than the vairiances of the individual samples, and the test will signal a significant difference. Thus the test uses variance as a tool to detect shifts in mean, not because it is interesed in the individual sample variances per se.
ANOVA is most appropriate when the sample data are approximately normal and the samples are distinguished by a nominal variable. For example, given a random sampling of the ages of members of five different political parties, a one-way ANOVA would be an appropriate test of the whether the different parties tend to attract different-aged memberships.
On the other hand, given data on the incomes and vacation lengths of a large number of people, dividing the people into five income quintiles and performing a one-way ANOVA to compare the vacation day distribution of each quintile would not be an appropriate way to test the hypothesis that richer people take longer vacations. Since income is a cardinal variable, it would be better to in this case of put the data into a BivariateSample and perform a test of association, such as a BivariateSample.PearsonRTest, BivariateSample.SpearmanRhoTest, or BivariateSample.KendallTauTest between the two variables. If you have measurements of additional variables for each indiviual, a MultivariateSample.LinearRegression(int) analysis would allow you to adjust for confounding effects of the other variables.
Referenced by Test.SampleTest.AnovaDistribution(), Test.SampleTest.AnovaStudentAgreement(), and Test.SampleTest.AnovaTest().
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Performs a one-way ANOVA.
samples | The samples to compare. |
For detailed information, see the variable argument overload.
References Meta.Numerics.MoreMath.Sqr().
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Performs a Kruskal-Wallis test on the given samples.
samples | The set of samples to compare. |
Kruskal-Wallis tests for differences between the samples. It is a non-parametric alternative to the one-way ANOVA (OneWayAnovaTest(Sample[])).
The test is essentially a one-way ANOVA performed on the ranks of sample values instead of the sample values themselves.
A Kruskal-Wallis test on two samples is equivilent to a Mann-Whitney test (see MannWhitneyTest).
Referenced by Test.SampleTest.KruskalWallis().
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Performs a Kruskal-Wallis test on the given samples.
samples | The set of samples to compare. |
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Tests whether the sample is compatible with the given distribution.
distribution | The test distribution. |
The null hypothesis of the KS test is that the sample is drawn from the given continuous distribution. The test statsitic D is the maximum deviation of the sample's emperical distribution function (EDF) from the distribution's cumulative distribution function (CDF). A high value of the test statistic, corresponding to a low right tail probability, indicates that the sample distribution disagrees with the given distribution to a degree unlikely to arise from statistical fluctuations.
For small sample sizes, we compute the null distribution of D exactly. For large sample sizes, we use an accurate asympotitc approximation. Therefore it is safe to use this method for all sample sizes.
ArgumentNullException | distribution is null. |
Referenced by Test.SampleTest.AnovaDistribution(), Test.BivariateSampleTest.BivariateLinearRegression(), Test.BivariateSampleTest.BivariateLinearRegressionGoodnessOfFitDistribution(), Test.MultivariateSampleTest.BivariateNullAssociation(), Test.DistributionTest.DistributionRandomDeviates(), Test.DataSetTest.FitDataToLineChiSquaredTest(), Test.DataSetTest.FitDataToPolynomialChiSquaredTest(), Meta.Numerics.Statistics.Distributions.NormalDistribution.FitToSample(), Test.DistributionTest.GammaFromExponential(), Test.DistributionTest.InverseGaussianSummation(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.MultivariateSampleTest.MultivariateLinearRegressionNullDistribution(), Test.BivariateSampleTest.PearsonRDistribution(), Test.SampleTest.SampleComparisonTest(), Test.SampleTest.SampleKolmogorovSmirnovTest(), Test.SampleTest.SampleKuiperTest(), Test.DistributionTest.StudentTest(), Test.DistributionTest.StudentTest2(), Test.RandomTest.TimeGammaGenerators(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), FutureTest.FutureTest.TwoSampleKS2(), Test.DistributionTest.UniformOrderStatistics(), and Test.SampleTest.ZTestDistribution().
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Tests whether the sample is compatible with the given distribution.
distribution | The test distribution. |
Referenced by FutureTest.FutureTest.ChiSquareDistribution(), Test.DistributionTest.FisherTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.SampleTest.SampleKuiperTest(), and Test.NullDistributionTests.SpearmanNullDistributionTest().
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Tests whether the sample is compatible with another sample.
b | The other sample. |
ArgumentNullException | b is null. |
References Meta.Numerics.Functions.AdvancedIntegerMath.BinomialCoefficient(), Meta.Numerics.Statistics.Sample.Count, Meta.Numerics.Statistics.Sample.data, and Meta.Numerics.Interval.FromEndpoints().
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Tests whether the variance of two samples is compatible.
a | The first sample. |
b | The second sample. |
References Meta.Numerics.Statistics.Sample.Count, and Meta.Numerics.Statistics.Sample.Variance.
Referenced by Test.SampleTest.SampleFisherFTest().
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Gets an enumerator of sample values.
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Performs a maximum likelihood fit.
distribution | The distribution to fit to the data. |
References Meta.Numerics.Matrices.SymmetricMatrix.CholeskyDecomposition(), Meta.Numerics.Analysis.SpaceExtremum.Curvature(), Meta.Numerics.Analysis.FunctionMath.FindMinimum(), Meta.Numerics.Statistics.Distributions.IParameterizedDistribution.GetParameters(), Meta.Numerics.Matrices.CholeskyDecomposition.Inverse(), Meta.Numerics.Statistics.Distributions.IParameterizedDistribution.Likelihood(), Meta.Numerics.Analysis.SpaceExtremum.Location(), and Meta.Numerics.Statistics.Distributions.IParameterizedDistribution.SetParameters().
Referenced by Test.SampleTest.SampleMaximumLikelihoodFit().
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Loads values from a data reader.
reader | The data reader. |
dbIndex | The column number. |
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Gets or sets the name of the sample.
Referenced by Test.SampleTest.SamplePopulationMomentEstimateVariances().
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Gets a value indicating whether the sample is read-only.
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Gets the number of values in the sample.
Referenced by Test.SampleTest.AnovaTest(), Meta.Numerics.Statistics.Sample.FisherFTest(), Test.DataSetTest.FitDataToLineChiSquaredTest(), Test.DataSetTest.FitDataToPolynomialChiSquaredTest(), Meta.Numerics.Statistics.Distributions.WaldDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.ExponentialDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.WeibullDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.NormalDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.LognormalDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.BetaDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.GammaDistribution.FitToSample(), Meta.Numerics.Statistics.Sample.KolmogorovSmirnovTest(), Test.SampleTest.LowSampleMoments(), Meta.Numerics.Statistics.Sample.MannWhitneyTest(), Test.SampleTest.SampleCopy(), Test.SampleTest.SampleManipulations(), Test.SampleTest.SampleMaximumLikelihoodFit(), Test.SampleTest.SampleMoments(), Test.SampleTest.SignTestDistribution(), Test.DistributionTest.StudentTest(), Meta.Numerics.Statistics.Sample.StudentTTest(), Test.SampleTest.TTestDistribution(), and Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest().
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Gets the sample mean.
The mean is the average of all values in the sample.
Referenced by Test.SampleTest.AnovaStudentAgreement(), Test.SampleTest.BetaFitUncertainty(), Test.ContingencyTableTest.ContingencyTableProbabilitiesAndUncertainties(), Test.SampleTest.ExponentialFitUncertainty(), Test.DataSetTest.FitDataToPolynomialUncertaintiesTest(), Meta.Numerics.Statistics.Distributions.WaldDistribution.FitToSample(), Test.SampleTest.GammaFitUncertainty(), Test.SampleTest.LowSampleMoments(), Test.MultivariateSampleTest.MultivariateMoments(), Test.RectangularMatrixTest.PC(), Test.MultivariateSampleTest.PrincipalComponentAnalysis(), Test.SampleTest.SampleMaximumLikelihoodFit(), Test.SampleTest.SamplePopulationMomentEstimateVariances(), Test.SampleTest.SampleTransform(), Test.DistributionTest.StudentTest(), Meta.Numerics.Statistics.Sample.StudentTTest(), and Test.SampleTest.WeibullFitUncertainties().
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Gets the sample variance.
Note this is the actual variance of the sample values, not the infered variance of the underlying population; to obtain the latter use PopulationVariance.
Referenced by Test.SampleTest.AnovaStudentAgreement(), Meta.Numerics.Statistics.Sample.FisherFTest(), Test.MultivariateSampleTest.GetTotalVariance(), Test.SampleTest.LowSampleMoments(), Test.MultivariateSampleTest.MultivariateMoments(), Test.RectangularMatrixTest.PC(), and Test.SampleTest.SampleTransform().
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Gets the sample standard deviation.
Note this is the actual standard deviation of the sample values, not the infered standard deviation of the underlying population; to obtain the latter use PopulationStandardDeviation.
Referenced by Test.DataSetTest.FitDataToPolynomialUncertaintiesTest().
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Gets the sample skewness.
Skewness is the third central moment, measured in units of the appropriate power of the standard deviation.
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Gets the sample median.
Referenced by Test.SampleTest.SampleMedian().
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Gets the interquartile range of sample measurmements.
The interquartile range is the interval between the 25th and the 75th percentile.
Referenced by Test.SampleTest.SampleInterquartileRange().
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Gets the smallest value in the sample.
Referenced by Meta.Numerics.Statistics.Distributions.WeibullDistribution.FitToSample(), Test.SampleTest.SampleMedian(), and Test.SampleTest.SampleTransform().
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Gets the largest value in the sample.
Referenced by Test.SampleTest.SampleMedian(), and Test.SampleTest.SampleTransform().
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Gets an estimate of the population mean from the sample.
Referenced by Test.SampleTest.AnovaDistribution(), Test.BivariateSampleTest.BivariateLinearRegression(), Test.BivariateSampleTest.BivariateLinearRegressionGoodnessOfFitDistribution(), Test.BivariateSampleTest.BivariatePolynomialRegression(), Test.ContingencyTableTest.ContingencyTableProbabilitiesAndUncertainties(), Test.DataSetTest.FitDataToPolynomialUncertaintiesTest(), Meta.Numerics.Statistics.Distributions.NormalDistribution.FitToSample(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.BivariateSampleTest.LinearLogisticRegression(), Test.MultivariateSampleTest.MultivariateNormalSummaryStatistics(), Test.SampleTest.NormalFitUncertainties(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleMoments(), Test.SampleTest.SamplePopulationMomentEstimateVariances(), Test.SampleTest.SignTestDistribution(), Test.NullDistributionTests.SpearmanNullDistributionTest(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), and Test.SampleTest.WaldFitUncertainties().
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Gets an estimate of the population variance from the sample.
Referenced by Test.BivariateSampleTest.BivariateLinearRegression(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.BivariateSampleTest.LinearLogisticRegression(), Test.MultivariateSampleTest.MultivariateNormalSummaryStatistics(), Test.SampleTest.NormalFitUncertainties(), Test.SampleTest.SamplePopulationMomentEstimateVariances(), Test.NullDistributionTests.SpearmanNullDistributionTest(), and Test.SampleTest.WaldFitUncertainties().
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Gets an estimate of the population standard deviation from the sample.
Referenced by Test.SampleTest.AnovaDistribution(), Test.SampleTest.BetaFitUncertainty(), Test.ContingencyTableTest.ContingencyTableProbabilitiesAndUncertainties(), Test.SampleTest.ExponentialFitUncertainty(), Test.DataSetTest.FitDataToPolynomialUncertaintiesTest(), Meta.Numerics.Statistics.Distributions.NormalDistribution.FitToSample(), Test.SampleTest.GammaFitUncertainty(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleMoments(), Test.SampleTest.SignTestDistribution(), Test.DistributionTest.StudentTest(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), and Test.SampleTest.WeibullFitUncertainties().