std/stats

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Statistical analysis framework for performing basic statistical analysis of data. The data is analysed in a single pass, when it is pushed to a RunningStat or RunningRegress object.

RunningStat calculates for a single data set

  • n (data count)
  • min (smallest value)
  • max (largest value)
  • sum
  • mean
  • variance
  • varianceS (sample variance)
  • standardDeviation
  • standardDeviationS (sample standard deviation)
  • skewness (the third statistical moment)
  • kurtosis (the fourth statistical moment)

RunningRegress calculates for two sets of data

  • n (data count)
  • slope
  • intercept
  • correlation

Procs are provided to calculate statistics on openArrays.

However, if more than a single statistical calculation is required, it is more efficient to push the data once to a RunningStat object and then call the numerous statistical procs for the RunningStat object:

Example:

import std/stats
from std/math import almostEqual

template `~=`(a, b: float): bool = almostEqual(a, b)

var statistics: RunningStat  ## Must be var
statistics.push(@[1.0, 2.0, 1.0, 4.0, 1.0, 4.0, 1.0, 2.0])
doAssert statistics.n == 8
doAssert statistics.mean() ~= 2.0
doAssert statistics.variance() ~= 1.5
doAssert statistics.varianceS() ~= 1.714285714285715
doAssert statistics.skewness() ~= 0.8164965809277261
doAssert statistics.skewnessS() ~= 1.018350154434631
doAssert statistics.kurtosis() ~= -1.0
doAssert statistics.kurtosisS() ~= -0.7000000000000008

Types

RunningStat = object
  n*: int                    ## amount of pushed data
  min*, max*, sum*: float    ## self-explaining
  mom1, mom2, mom3, mom4: float ## statistical moments, mom1 is mean
  
An accumulator for statistical data.   Source   Edit
RunningRegress = object
  n*: int                    ## amount of pushed data
  x_stats*: RunningStat      ## stats for the first set of data
  y_stats*: RunningStat      ## stats for the second set of data
  s_xy: float                ## accumulated data for combined xy
  
An accumulator for regression calculations.   Source   Edit

Procs

proc clear(s: var RunningStat) {....raises: [], tags: [].}
Resets s.   Source   Edit
proc push(s: var RunningStat; x: float) {....raises: [], tags: [].}
Pushes a value x for processing.   Source   Edit
proc push(s: var RunningStat; x: int) {....raises: [], tags: [].}

Pushes a value x for processing.

x is simply converted to float and the other push operation is called.

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proc push(s: var RunningStat; x: openArray[float | int])

Pushes all values of x for processing.

Int values of x are simply converted to float and the other push operation is called.

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proc mean(s: RunningStat): float {....raises: [], tags: [].}
Computes the current mean of s.   Source   Edit
proc variance(s: RunningStat): float {....raises: [], tags: [].}
Computes the current population variance of s.   Source   Edit
proc varianceS(s: RunningStat): float {....raises: [], tags: [].}
Computes the current sample variance of s.   Source   Edit
proc standardDeviation(s: RunningStat): float {....raises: [], tags: [].}
Computes the current population standard deviation of s.   Source   Edit
proc standardDeviationS(s: RunningStat): float {....raises: [], tags: [].}
Computes the current sample standard deviation of s.   Source   Edit
proc skewness(s: RunningStat): float {....raises: [], tags: [].}
Computes the current population skewness of s.   Source   Edit
proc skewnessS(s: RunningStat): float {....raises: [], tags: [].}
Computes the current sample skewness of s.   Source   Edit
proc kurtosis(s: RunningStat): float {....raises: [], tags: [].}
Computes the current population kurtosis of s.   Source   Edit
proc kurtosisS(s: RunningStat): float {....raises: [], tags: [].}
Computes the current sample kurtosis of s.   Source   Edit
proc `+`(a, b: RunningStat): RunningStat {....raises: [], tags: [].}

Combines two RunningStats.

Useful when performing parallel analysis of data series and needing to re-combine parallel result sets.

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proc `+=`(a: var RunningStat; b: RunningStat) {.inline, ...raises: [], tags: [].}
Adds the RunningStat b to a.   Source   Edit
proc `$`(a: RunningStat): string {....raises: [], tags: [].}
Produces a string representation of the RunningStat. The exact format is currently unspecified and subject to change. Currently it contains:
  • the number of probes
  • min, max values
  • sum, mean and standard deviation.
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proc mean[T](x: openArray[T]): float
Computes the mean of x.   Source   Edit
proc variance[T](x: openArray[T]): float
Computes the population variance of x.   Source   Edit
proc varianceS[T](x: openArray[T]): float
Computes the sample variance of x.   Source   Edit
proc standardDeviation[T](x: openArray[T]): float
Computes the population standard deviation of x.   Source   Edit
proc standardDeviationS[T](x: openArray[T]): float
Computes the sample standard deviation of x.   Source   Edit
proc skewness[T](x: openArray[T]): float
Computes the population skewness of x.   Source   Edit
proc skewnessS[T](x: openArray[T]): float
Computes the sample skewness of x.   Source   Edit
proc kurtosis[T](x: openArray[T]): float
Computes the population kurtosis of x.   Source   Edit
proc kurtosisS[T](x: openArray[T]): float
Computes the sample kurtosis of x.   Source   Edit
proc clear(r: var RunningRegress) {....raises: [], tags: [].}
Resets r.   Source   Edit
proc push(r: var RunningRegress; x, y: float) {....raises: [], tags: [].}
Pushes two values x and y for processing.   Source   Edit
proc push(r: var RunningRegress; x, y: int) {.inline, ...raises: [], tags: [].}

Pushes two values x and y for processing.

x and y are converted to float and the other push operation is called.

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proc push(r: var RunningRegress; x, y: openArray[float | int])
Pushes two sets of values x and y for processing.   Source   Edit
proc slope(r: RunningRegress): float {....raises: [], tags: [].}
Computes the current slope of r.   Source   Edit
proc intercept(r: RunningRegress): float {....raises: [], tags: [].}
Computes the current intercept of r.   Source   Edit
proc correlation(r: RunningRegress): float {....raises: [], tags: [].}
Computes the current correlation of the two data sets pushed into r.   Source   Edit
proc `+`(a, b: RunningRegress): RunningRegress {....raises: [], tags: [].}

Combines two RunningRegress objects.

Useful when performing parallel analysis of data series and needing to re-combine parallel result sets

  Source   Edit
proc `+=`(a: var RunningRegress; b: RunningRegress) {....raises: [], tags: [].}
Adds the RunningRegress b to a.   Source   Edit