Statistics Class |
Extension methods to return basic statistics on set of data.
Inheritance HierarchyNamespace: Altaxo.Calc.Statistics
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public static class Statistics
The Statistics type exposes the following members.
Methods| Name | Description | |
|---|---|---|
 | Covariance(IEnumerableDouble, IEnumerableDouble) | Estimates the unbiased population covariance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
| Covariance(IEnumerableNullableDouble, IEnumerableNullableDouble) | Estimates the unbiased population covariance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. Null-entries are ignored. |
| Covariance(IEnumerableSingle, IEnumerableSingle) | Estimates the unbiased population covariance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
| EmpiricalCDF(IEnumerableDouble, Double) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalCDF(IEnumerableNullableDouble, Double) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalCDF(IEnumerableSingle, Single) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalCDFFunc(IEnumerableDouble) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalCDFFunc(IEnumerableNullableDouble) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalCDFFunc(IEnumerableSingle) | Estimates the empirical cumulative distribution function (CDF) at x from the provided samples. |
| EmpiricalInvCDF(IEnumerableDouble, Double) | Estimates the empirical inverse CDF at tau from the provided samples. |
| EmpiricalInvCDF(IEnumerableNullableDouble, Double) | Estimates the empirical inverse CDF at tau from the provided samples. |
| EmpiricalInvCDF(IEnumerableSingle, Double) | Estimates the empirical inverse CDF at tau from the provided samples. |
| EmpiricalInvCDFFunc(IEnumerableDouble) | Estimates the empirical inverse CDF at tau from the provided samples. |
| EmpiricalInvCDFFunc(IEnumerableNullableDouble) | Estimates the empirical inverse CDF at tau from the provided samples. |
| EmpiricalInvCDFFunc(IEnumerableSingle) | Estimates the empirical inverse CDF at tau from the provided samples. |
  | Entropy(IEnumerableDouble) | Calculates the entropy of a stream of double values in bits. Returns NaN if any of the values in the stream are NaN. |
| Entropy(IEnumerableNullableDouble) | Calculates the entropy of a stream of double values in bits. Returns NaN if any of the values in the stream are NaN. Null-entries are ignored. |
| FiveNumberSummary(IEnumerableDouble) | Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| FiveNumberSummary(IEnumerableNullableDouble) | Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| FiveNumberSummary(IEnumerableSingle) | Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| GeometricMean(IEnumerableDouble) | Evaluates the geometric mean. Returns NaN if data is empty or if any entry is NaN. |
| GeometricMean(IEnumerableSingle) | Evaluates the geometric mean. Returns NaN if data is empty or if any entry is NaN. |
| HarmonicMean(IEnumerableDouble) | Evaluates the harmonic mean. Returns NaN if data is empty or if any entry is NaN. |
| HarmonicMean(IEnumerableSingle) | Evaluates the harmonic mean. Returns NaN if data is empty or if any entry is NaN. |
| InterquartileRange(IEnumerableDouble) | Estimates the inter-quartile range from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| InterquartileRange(IEnumerableNullableDouble) | Estimates the inter-quartile range from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| InterquartileRange(IEnumerableSingle) | Estimates the inter-quartile range from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| Kurtosis(IEnumerableDouble) | Estimates the unbiased population kurtosis from the provided samples. Uses a normalizer (Bessel's correction; type 2). Returns NaN if data has less than four entries or if any entry is NaN. |
| Kurtosis(IEnumerableNullableDouble) | Estimates the unbiased population kurtosis from the provided samples. Uses a normalizer (Bessel's correction; type 2). Returns NaN if data has less than four entries or if any entry is NaN. Null-entries are ignored. |
| LowerQuartile(IEnumerableDouble) | Estimates the first quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| LowerQuartile(IEnumerableNullableDouble) | Estimates the first quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| LowerQuartile(IEnumerableSingle) | Estimates the first quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| Maximum(IEnumerableDouble) | Returns the maximum value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| Maximum(IEnumerableNullableDouble) | Returns the maximum value in the sample data. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| Maximum(IEnumerableSingle) | Returns the maximum value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MaximumAbsolute(IEnumerableDouble) | Returns the maximum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MaximumAbsolute(IEnumerableSingle) | Returns the maximum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MaximumMagnitudePhase(IEnumerableComplex32) | Returns the maximum magnitude and phase value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MaximumMagnitudePhase(IEnumerableComplex) | Returns the maximum magnitude and phase value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| Mean(IEnumerableDouble) | Evaluates the sample mean, an estimate of the population mean. Returns NaN if data is empty or if any entry is NaN. |
| Mean(IEnumerableNullableDouble) | Evaluates the sample mean, an estimate of the population mean. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| Mean(IEnumerableSingle) | Evaluates the sample mean, an estimate of the population mean. Returns NaN if data is empty or if any entry is NaN. |
| MeanStandardDeviation(IEnumerableDouble) | Estimates the sample mean and the unbiased population standard deviation from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN for mean if data is empty or if any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN. |
| MeanStandardDeviation(IEnumerableSingle) | Estimates the sample mean and the unbiased population standard deviation from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN for mean if data is empty or if any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN. |
| MeanVariance(IEnumerableDouble) | Estimates the sample mean and the unbiased population variance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN for mean if data is empty or if any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN. |
| MeanVariance(IEnumerableSingle) | Estimates the sample mean and the unbiased population variance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN for mean if data is empty or if any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN. |
| Median(IEnumerableDouble) | Estimates the sample median from the provided samples (R8). |
| Median(IEnumerableNullableDouble) | Estimates the sample median from the provided samples (R8). |
| Median(IEnumerableSingle) | Estimates the sample median from the provided samples (R8). |
| Minimum(IEnumerableDouble) | Returns the minimum value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| Minimum(IEnumerableNullableDouble) | Returns the minimum value in the sample data. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| Minimum(IEnumerableSingle) | Returns the minimum value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MinimumAbsolute(IEnumerableDouble) | Returns the minimum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MinimumAbsolute(IEnumerableSingle) | Returns the minimum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MinimumMagnitudePhase(IEnumerableComplex32) | Returns the minimum magnitude and phase value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MinimumMagnitudePhase(IEnumerableComplex) | Returns the minimum magnitude and phase value in the sample data. Returns NaN if data is empty or if any entry is NaN. |
| MovingAverage | Evaluates the sample mean over a moving window, for each samples. Returns NaN if no data is empty or if any entry is NaN. |
| OrderStatistic(IEnumerableDouble, Int32) | Returns the order statistic (order 1..N) from the provided samples. |
| OrderStatistic(IEnumerableSingle, Int32) | Returns the order statistic (order 1..N) from the provided samples. |
| OrderStatisticFunc(IEnumerableDouble) | Returns the order statistic (order 1..N) from the provided samples. |
| OrderStatisticFunc(IEnumerableSingle) | Returns the order statistic (order 1..N) from the provided samples. |
| Percentile(IEnumerableDouble, Int32) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| Percentile(IEnumerableNullableDouble, Int32) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| Percentile(IEnumerableSingle, Int32) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| PercentileFunc(IEnumerableDouble) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| PercentileFunc(IEnumerableNullableDouble) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| PercentileFunc(IEnumerableSingle) | Estimates the p-Percentile value from the provided samples. If a non-integer Percentile is needed, use Quantile instead. Approximately median-unbiased regardless of the sample distribution (R8). |
| PopulationCovariance(IEnumerableDouble, IEnumerableDouble) | Evaluates the population covariance from the provided full populations. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| PopulationCovariance(IEnumerableNullableDouble, IEnumerableNullableDouble) | Evaluates the population covariance from the provided full populations. On a dataset of size N will use an N normalize and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| PopulationCovariance(IEnumerableSingle, IEnumerableSingle) | Evaluates the population covariance from the provided full populations. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| PopulationKurtosis(IEnumerableDouble) | Evaluates the kurtosis from the full population. Does not use a normalizer and would thus be biased if applied to a subset (type 1). Returns NaN if data has less than three entries or if any entry is NaN. |
| PopulationKurtosis(IEnumerableNullableDouble) | Evaluates the kurtosis from the full population. Does not use a normalizer and would thus be biased if applied to a subset (type 1). Returns NaN if data has less than three entries or if any entry is NaN. Null-entries are ignored. |
| PopulationSkewness(IEnumerableDouble) | Evaluates the skewness from the full population. Does not use a normalizer and would thus be biased if applied to a subset (type 1). Returns NaN if data has less than two entries or if any entry is NaN. |
| PopulationSkewness(IEnumerableNullableDouble) | Evaluates the skewness from the full population. Does not use a normalizer and would thus be biased if applied to a subset (type 1). Returns NaN if data has less than two entries or if any entry is NaN. Null-entries are ignored. |
| PopulationSkewnessKurtosis | Evaluates the skewness and kurtosis from the full population. Does not use a normalizer and would thus be biased if applied to a subset (type 1). |
| PopulationStandardDeviation(IEnumerableDouble) | Evaluates the standard deviation from the provided full population. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| PopulationStandardDeviation(IEnumerableNullableDouble) | Evaluates the standard deviation from the provided full population. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| PopulationStandardDeviation(IEnumerableSingle) | Evaluates the standard deviation from the provided full population. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| PopulationVariance(IEnumerableDouble) | Evaluates the variance from the provided full population. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| PopulationVariance(IEnumerableNullableDouble) | Evaluates the variance from the provided full population. On a dataset of size N will use an N normalize and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| PopulationVariance(IEnumerableSingle) | Evaluates the variance from the provided full population. On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset. Returns NaN if data is empty or if any entry is NaN. |
| Quantile(IEnumerableDouble, Double) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| Quantile(IEnumerableNullableDouble, Double) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| Quantile(IEnumerableSingle, Double) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| QuantileCustom(IEnumerableDouble, Double, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileCustom(IEnumerableNullableDouble, Double, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileCustom(IEnumerableSingle, Double, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileCustomFunc(IEnumerableDouble, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileCustomFunc(IEnumerableNullableDouble, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileCustomFunc(IEnumerableSingle, QuantileDefinition) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileFunc(IEnumerableDouble) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| QuantileFunc(IEnumerableNullableDouble) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| QuantileFunc(IEnumerableSingle) | Estimates the tau-th quantile from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. Approximately median-unbiased regardless of the sample distribution (R8). |
| QuantileRank(IEnumerableDouble, Double, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileRank(IEnumerableNullableDouble, Double, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileRank(IEnumerableSingle, Single, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileRankFunc(IEnumerableDouble, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileRankFunc(IEnumerableNullableDouble, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| QuantileRankFunc(IEnumerableSingle, RankDefinition) | Estimates the quantile tau from the provided samples. The tau-th quantile is the data value where the cumulative distribution function crosses tau. The quantile definition can be specified to be compatible with an existing system. |
| Ranks(IEnumerableDouble, RankDefinition) | Evaluates the rank of each entry of the provided samples. The rank definition can be specified to be compatible with an existing system. |
| Ranks(IEnumerableNullableDouble, RankDefinition) | Evaluates the rank of each entry of the provided samples. The rank definition can be specified to be compatible with an existing system. |
| Ranks(IEnumerableSingle, RankDefinition) | Evaluates the rank of each entry of the provided samples. The rank definition can be specified to be compatible with an existing system. |
| RootMeanSquare(IEnumerableDouble) | Evaluates the root mean square (RMS) also known as quadratic mean. Returns NaN if data is empty or if any entry is NaN. |
| RootMeanSquare(IEnumerableNullableDouble) | Evaluates the root mean square (RMS) also known as quadratic mean. Returns NaN if data is empty or if any entry is NaN. Null-entries are ignored. |
| RootMeanSquare(IEnumerableSingle) | Evaluates the root mean square (RMS) also known as quadratic mean. Returns NaN if data is empty or if any entry is NaN. |
| Skewness(IEnumerableDouble) | Estimates the unbiased population skewness from the provided samples. Uses a normalizer (Bessel's correction; type 2). Returns NaN if data has less than three entries or if any entry is NaN. |
| Skewness(IEnumerableNullableDouble) | Estimates the unbiased population skewness from the provided samples. Uses a normalizer (Bessel's correction; type 2). Returns NaN if data has less than three entries or if any entry is NaN. Null-entries are ignored. |
| SkewnessKurtosis | Estimates the unbiased population skewness and kurtosis from the provided samples in a single pass. Uses a normalizer (Bessel's correction; type 2). |
| StandardDeviation(IEnumerableDouble) | Estimates the unbiased population standard deviation from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
| StandardDeviation(IEnumerableNullableDouble) | Estimates the unbiased population standard deviation from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. Null-entries are ignored. |
| StandardDeviation(IEnumerableSingle) | Estimates the unbiased population standard deviation from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
| UpperQuartile(IEnumerableDouble) | Estimates the third quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| UpperQuartile(IEnumerableNullableDouble) | Estimates the third quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| UpperQuartile(IEnumerableSingle) | Estimates the third quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8). |
| Variance(IEnumerableDouble) | Estimates the unbiased population variance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
| Variance(IEnumerableNullableDouble) | Estimates the unbiased population variance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. Null-entries are ignored. |
| Variance(IEnumerableSingle) | Estimates the unbiased population variance from the provided samples. On a dataset of size N will use an N-1 normalizer (Bessel's correction). Returns NaN if data has less than two entries or if any entry is NaN. |
See Also