std/stats

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

Imports

math

Types

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
  ## accumulated data for combined xy

An accumulator for regression calculations. Source Edit

RunningStat = object
  n*: int                    ## amount of pushed data
  min*, max*, sum*: float    ## self-explaining
  ## statistical moments, mom1 is mean

An accumulator for statistical data. Source Edit

Procs

proc `$`(a: RunningStat): string {....raises: [], tags: [], forbids: [].}

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.

Source Edit

proc `+`(a, b: RunningRegress): RunningRegress {....raises: [], tags: [],
    forbids: [].}

Combines two RunningRegress objects.

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

Source Edit

proc `+`(a, b: RunningStat): RunningStat {....raises: [], tags: [], forbids: [].}

Combines two RunningStats.

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: [],
    forbids: [].}

Adds the RunningRegress b to a. Source Edit

proc `+=`(a: var RunningStat; b: RunningStat) {.inline, ...raises: [], tags: [],
    forbids: [].}

Adds the RunningStat b to a. Source Edit

proc clear(r: var RunningRegress) {....raises: [], tags: [], forbids: [].}

Resets r. Source Edit

proc clear(s: var RunningStat) {....raises: [], tags: [], forbids: [].}

Resets s. Source Edit

proc correlation(r: RunningRegress): float {....raises: [], tags: [], forbids: [].}

Computes the current correlation of the two data sets pushed into r. Source Edit

proc intercept(r: RunningRegress): float {....raises: [], tags: [], forbids: [].}

Computes the current intercept of r. Source Edit

proc kurtosis(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current population kurtosis of s. Source Edit

proc kurtosis[T](x: openArray[T]): float

Computes the population kurtosis of x. Source Edit

proc kurtosisS(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current sample kurtosis of s. Source Edit

proc kurtosisS[T](x: openArray[T]): float

Computes the sample kurtosis of x. Source Edit

proc mean(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current mean of s. Source Edit

proc mean[T](x: openArray[T]): float

Computes the mean of x. Source Edit

proc push(r: var RunningRegress; x, y: float) {....raises: [], tags: [],
    forbids: [].}

Pushes two values x and y for processing. Source Edit

proc push(r: var RunningRegress; x, y: int) {.inline, ...raises: [], tags: [],
    forbids: [].}

Pushes two values x and y for processing.

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

Source Edit

proc push(r: var RunningRegress; x, y: openArray[float | int])

Pushes two sets of values x and y for processing. Source Edit

proc push(s: var RunningStat; x: float) {....raises: [], tags: [], forbids: [].}

Pushes a value x for processing. Source Edit

proc push(s: var RunningStat; x: int) {....raises: [], tags: [], forbids: [].}

Pushes a value x for processing.

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

Source Edit

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.

Source Edit

proc skewness(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current population skewness of s. Source Edit

proc skewness[T](x: openArray[T]): float

Computes the population skewness of x. Source Edit

proc skewnessS(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current sample skewness of s. Source Edit

proc skewnessS[T](x: openArray[T]): float

Computes the sample skewness of x. Source Edit

proc slope(r: RunningRegress): float {....raises: [], tags: [], forbids: [].}

Computes the current slope of r. Source Edit

proc standardDeviation(s: RunningStat): float {....raises: [], tags: [],
    forbids: [].}

Computes the current population standard deviation of s. Source Edit

proc standardDeviation[T](x: openArray[T]): float

Computes the population standard deviation of x. Source Edit

proc standardDeviationS(s: RunningStat): float {....raises: [], tags: [],
    forbids: [].}

Computes the current sample standard deviation of s. Source Edit

proc standardDeviationS[T](x: openArray[T]): float

Computes the sample standard deviation of x. Source Edit

proc variance(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current population variance of s. Source Edit

proc variance[T](x: openArray[T]): float

Computes the population variance of x. Source Edit

proc varianceS(s: RunningStat): float {....raises: [], tags: [], forbids: [].}

Computes the current sample variance of s. Source Edit

proc varianceS[T](x: openArray[T]): float

Computes the sample variance of x. Source Edit