Seq (FSharp.Stats)

Seq Module

Namespace: FSharp.Stats
Assembly: FSharp.Stats.dll

Module to compute common statistical measure

Nested modules

Modules	Description
UtilityFunctions	A module which implements helper functions to provide special statistical measures

Functions and values

Function or value	Description
`cov seq1 seq2` Full Usage: `cov seq1 seq2` Parameters: seq1 : `seq<^T>` - The first input sequence. seq2 : `seq<^T>` - The second input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1) Modifiers: inline Type parameters: ^T, ^b, ^U	Computes the sample covariance of two random variables Returns NaN if data is empty or if any entry is NaN. seq1 : `seq<^T>` The first input sequence. seq2 : `seq<^T>` The second input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1)
`covBy f seq` Full Usage: `covBy f seq` Parameters: f : `'T -> ^a * ^a` - A function applied to transform each element of the input sequence into a tuple of paired observations. seq : `seq<'T>` - The input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1) Modifiers: inline	Computes the sample covariance of two random variables generated by applying a function to the input sequence. Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a * ^a` A function applied to transform each element of the input sequence into a tuple of paired observations. seq : `seq<'T>` The input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1) Example `// To get the sample covariance between x and y observations: let xy = [ {\| x = 5.; y = 2. \|} {\| x = 12.; y = 8. \|} {\| x = 18.; y = 18. \|} {\| x = -23.; y = -20. \|} {\| x = 45.; y = 28. \|} ] xy \|> Seq.covBy (fun x -> x.x, x.y) // evaluates to 434.90`
`covOfPairs seq` Full Usage: `covOfPairs seq` Parameters: seq : `seq<^T * ^T>` - The input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1) Modifiers: inline	Computes the sample covariance of two random variables. The covariance will be calculated between the paired observations. Returns NaN if data is empty or if any entry is NaN. seq : `seq<^T * ^T>` The input sequence. Returns: `^U` sample covariance estimator (Bessel's correction by N-1) Example `// Consider a sequence of paired x and y values: // [(x1, y1); (x2, y2); (x3, y3); (x4, y4); ... ] let xy = [(5., 2.); (12., 8.); (18., 18.); (-23., -20.); (45., 28.)] // To get the sample covariance between x and y: xy \|> Seq.covOfPairs // evaluates to 434.90`
`covPopulation seq1 seq2` Full Usage: `covPopulation seq1 seq2` Parameters: seq1 : `seq<^T>` - The first input sequence. seq2 : `seq<^T>` - The second input sequence. Returns: `^U` population covariance estimator (denominator N) Modifiers: inline Type parameters: ^T, ^b, ^U	Computes the population covariance of two random variables Returns NaN if data is empty or if any entry is NaN. seq1 : `seq<^T>` The first input sequence. seq2 : `seq<^T>` The second input sequence. Returns: `^U` population covariance estimator (denominator N)
`covPopulationBy f seq` Full Usage: `covPopulationBy f seq` Parameters: f : `'T -> ^a * ^a` - A function applied to transform each element of the input sequence into a tuple of paired observations. seq : `seq<'T>` - The input sequence. Returns: `^U` population covariance estimator (denominator N) Modifiers: inline	Computes the population covariance of two random variables generated by applying a function to the input sequence. Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a * ^a` A function applied to transform each element of the input sequence into a tuple of paired observations. seq : `seq<'T>` The input sequence. Returns: `^U` population covariance estimator (denominator N) Example `// To get the population covariance between x and y observations: let xy = [ {\| x = 5.; y = 2. \|} {\| x = 12.; y = 8. \|} {\| x = 18.; y = 18. \|} {\| x = -23.; y = -20. \|} {\| x = 45.; y = 28. \|} ] xy \|> Seq.covPopulationBy (fun x -> x.x, x.y) // evaluates to 347.92`
`covPopulationOfPairs seq` Full Usage: `covPopulationOfPairs seq` Parameters: seq : `seq<^T * ^T>` - The input sequence. Returns: `^U` population covariance estimator (denominator N) Modifiers: inline	Computes the population covariance of two random variables. The covariance will be calculated between the paired observations. Returns NaN if data is empty or if any entry is NaN. seq : `seq<^T * ^T>` The input sequence. Returns: `^U` population covariance estimator (denominator N) Example `// Consider a sequence of paired x and y values: // [(x1, y1); (x2, y2); (x3, y3); (x4, y4); ... ] let xy = [(5., 2.); (12., 8.); (18., 18.); (-23., -20.); (45., 28.)] // To get the population covariance between x and y: xy \|> Seq.covPopulationOfPairs // evaluates to 347.92`
`cv items` Full Usage: `cv items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` Coefficient of Variation of a sample (Bessel's correction by N-1) Modifiers: inline Type parameters: ^T, ^U, ^b, ^c	Computes the Coefficient of Variation of a sample (Bessel's correction by N-1) Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` Coefficient of Variation of a sample (Bessel's correction by N-1)
`cvBy f items` Full Usage: `cvBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` Coefficient of Variation of a sample (Bessel's correction by N-1) Modifiers: inline	Computes the Coefficient of Variation of a sample (Bessel's correction by N-1) Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` Coefficient of Variation of a sample (Bessel's correction by N-1)
`cvPopulation items` Full Usage: `cvPopulation items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` Coefficient of Variation of the population Modifiers: inline	Computes the Coefficient of Variation of the population (population standard deviation) Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` Coefficient of Variation of the population
`cvPopulationBy f items` Full Usage: `cvPopulationBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` Coefficient of Variation of the population Modifiers: inline	Computes the Coefficient of Variation of the population (population standard deviation) Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` Coefficient of Variation of the population
`getCvOfReplicates rep data` Full Usage: `getCvOfReplicates rep data` Parameters: rep : `int` - data : `seq<^a>` - Returns: `seq<^a0>` Modifiers: inline Type parameters: ^a, ^a, ^b, ^c	calculates the coefficient of variation based on the sample standard deviations with a given number of replicates present in the sequence rep : `int` data : `seq<^a>` Returns: `seq<^a0>` Example
`getMeanOfReplicates rep data` Full Usage: `getMeanOfReplicates rep data` Parameters: rep : `int` - data : `seq<^a>` - Returns: `seq<^a0>` Modifiers: inline Type parameters: ^a, ^a	calculates the sample means with a given number of replicates present in the sequence rep : `int` data : `seq<^a>` Returns: `seq<^a0>` Example
`getStDevOfReplicates rep data` Full Usage: `getStDevOfReplicates rep data` Parameters: rep : `int` - data : `seq<^a>` - Returns: `seq<^c>` Modifiers: inline Type parameters: ^a, ^a, ^b, ^c	calculates the sample standard deviations with a given number of replicates present in the sequence rep : `int` data : `seq<^a>` Returns: `seq<^c>` Example
`mean items` Full Usage: `mean items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` population mean (Normalized by N) Modifiers: inline Type parameters: ^T, ^U	Computes the population mean (Normalized by N) Returns default value if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` population mean (Normalized by N)
`meanBy f items` Full Usage: `meanBy f items` Parameters: f : `'T -> ^U` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` population mean (Normalized by N) Modifiers: inline Type parameters: 'T, ^U	Computes the population mean (Normalized by N)s Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^U` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` population mean (Normalized by N)
`meanGeometric items` Full Usage: `meanGeometric items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` gemetric mean Modifiers: inline Type parameters: ^T, ^U	Computes gemetric mean Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` gemetric mean
`meanGeometricBy f items` Full Usage: `meanGeometricBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` gemetric mean Modifiers: inline	Computes gemetric mean Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` gemetric mean
`meanHarmonic items` Full Usage: `meanHarmonic items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` harmonic mean Modifiers: inline	Computes harmonic mean Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` harmonic mean
`meanHarmonicBy f items` Full Usage: `meanHarmonicBy f items` Parameters: f : `'T -> ^U` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` harmonic mean Modifiers: inline Type parameters: 'T, ^U	Computes harmonic mean Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^U` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` harmonic mean
`meanQuadratic items` Full Usage: `meanQuadratic items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` quadratic mean Modifiers: inline	Computes quadratic mean Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` quadratic mean
`meanQuadraticBy f items` Full Usage: `meanQuadraticBy f items` Parameters: f : `^a -> ^b` - A function applied to transform each element of the sequence. items : `seq<^T>` - The input sequence. Returns: `^U` quadratic mean Modifiers: inline	Computes quadratic mean Returns NaN if data is empty or if any entry is NaN. f : `^a -> ^b` A function applied to transform each element of the sequence. items : `seq<^T>` The input sequence. Returns: `^U` quadratic mean
`meanTruncated percent data` Full Usage: `meanTruncated percent data` Parameters: percent : `float` data : `seq<^T>` Returns: `^U` truncated (trimmed) mean Modifiers: inline Type parameters: ^T, ^U	Computes the truncated (trimmed) mean where x percent of the highest, and x percent of the lowest values are discarded (total 2x) Returns NaN if data is empty or if any entry is NaN. percent : `float` data : `seq<^T>` Returns: `^U` truncated (trimmed) mean
`meanTruncatedBy f percent data` Full Usage: `meanTruncatedBy f percent data` Parameters: f : `'T -> ^U` - A function applied to transform each element of the sequence. percent : `float` data : `seq<'T>` Returns: `^U` truncated (trimmed) mean Modifiers: inline Type parameters: 'T, ^U	Computes the truncated (trimmed) mean Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^U` A function applied to transform each element of the sequence. percent : `float` data : `seq<'T>` Returns: `^U` truncated (trimmed) mean
`median items` Full Usage: `median items` Parameters: items : `seq<^T>` - Returns: `^T` Modifiers: inline Type parameters: ^T, ^a	Sample Median items : `seq<^T>` Returns: `^T` Example
`medianAbsoluteDev data` Full Usage: `medianAbsoluteDev data` Parameters: data : `seq<float>` - Returns: `float`	Median absolute deviation (MAD) data : `seq<float>` Returns: `float` Example
`range items` Full Usage: `range items` Parameters: items : `seq<'a>` Returns: `Interval<'a>` Modifiers: inline Type parameters: 'a	items : `seq<'a>` Returns: `Interval<'a>`
`rangeBy f items` Full Usage: `rangeBy f items` Parameters: f : `'a -> 'b` items : `seq<'a>` Returns: `Interval<'a>` Modifiers: inline	f : `'a -> 'b` items : `seq<'a>` Returns: `Interval<'a>`
`sem items` Full Usage: `sem items` Parameters: items : `seq<^T>` - Returns: `float` Modifiers: inline	Computes the standard error of the mean (SEM) with bessel corrected sample standard deviation items : `seq<^T>` Returns: `float` Example
`stDev items` Full Usage: `stDev items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` standard deviation of a sample (Bessel's correction by N-1) Modifiers: inline Type parameters: ^T, ^a, ^b, ^U	Computes the sample standard deviation Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` standard deviation of a sample (Bessel's correction by N-1)
`stDevBy f items` Full Usage: `stDevBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` standard deviation of a sample (Bessel's correction by N-1) Modifiers: inline	Computes the sample standard deviation Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` standard deviation of a sample (Bessel's correction by N-1)
`stDevPopulation items` Full Usage: `stDevPopulation items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` population standard deviation (denominator = N) Modifiers: inline Type parameters: ^T, ^a, ^b, ^U	Computes the population standard deviation (denominator = N) Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` population standard deviation (denominator = N)
`stDevPopulationBy f items` Full Usage: `stDevPopulationBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` population standard deviation (denominator = N) Modifiers: inline	Computes the population standard deviation (denominator = N) Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` population standard deviation (denominator = N)
`stats items` Full Usage: `stats items` Parameters: items : `seq<^T>` - Returns: `SummaryStats<^T>` Modifiers: inline Type parameters: ^T, ^a, ^b	Returns SummeryStats of deq with N, mean, sum-of-squares, minimum and maximum items : `seq<^T>` Returns: `SummaryStats<^T>` Example
`var items` Full Usage: `var items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` variance of a sample (Bessel's correction by N-1) Modifiers: inline Type parameters: ^T, ^U, ^a	Computes the sample variance (Bessel's correction by N-1) Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` variance of a sample (Bessel's correction by N-1)
`varBy f items` Full Usage: `varBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` variance of a sample (Bessel's correction by N-1) Modifiers: inline	Computes the sample variance (Bessel's correction by N-1) Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` variance of a sample (Bessel's correction by N-1)
`varPopulation items` Full Usage: `varPopulation items` Parameters: items : `seq<^T>` - The input sequence. Returns: `^U` population variance estimator (denominator N) Modifiers: inline Type parameters: ^T, ^U, ^a	Computes variance of the given values (denominator N) Returns NaN if data is empty or if any entry is NaN. items : `seq<^T>` The input sequence. Returns: `^U` population variance estimator (denominator N)
`varPopulationBy f items` Full Usage: `varPopulationBy f items` Parameters: f : `'T -> ^a` - A function applied to transform each element of the sequence. items : `seq<'T>` - The input sequence. Returns: `^U` population variance estimator (denominator N) Modifiers: inline	Computes variance of the given values (denominator N) Returns NaN if data is empty or if any entry is NaN. f : `'T -> ^a` A function applied to transform each element of the sequence. items : `seq<'T>` The input sequence. Returns: `^U` population variance estimator (denominator N)
`weightedMean weights items` Full Usage: `weightedMean weights items` Parameters: weights : `seq<^T>` items : `seq<^T>` Returns: `^c -> ^b` Modifiers: inline	Computes the Weighted Mean of the given values. weights : `seq<^T>` items : `seq<^T>` Returns: `^c -> ^b`

Seq Module

Nested modules

Functions and values

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