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

RunningStat calculates for a single data set

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

RunningRegress calculates for two sets of data

n
slope
intercept
correlation

Procs have been provided to calculate statistics on arrays and sequences.

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

var rs: RunningStat
rs.push(MySeqOfData)
rs.mean()
rs.variance()
rs.skewness()
rs.kurtosis()

Examples:

static :
  block:
    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
    template `===`(a, b: float): bool =
      (abs(a - b) < 1e-009)

    doAssert statistics.mean() === 2.0
    doAssert statistics.variance() === 1.5
    doAssert statistics.varianceS() === 1.714285714285715
    doAssert statistics.skewness() === 0.8164965809277262
    doAssert statistics.skewnessS() === 1.018350154434631
    doAssert statistics.kurtosis() === -1.0
    doAssert statistics.kurtosisS() === -0.7000000000000008

Imports

Types

RunningStat = object n*: int ## number 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 ## number of pushed data x_stats*: RunningStat ## stats for first set of data y_stats*: RunningStat ## stats for 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: [].}

reset 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.

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.

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: [].}

combine two RunningStats.

Useful if performing parallel analysis of data series and need to re-combine parallel result sets

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

add a second RunningStats 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.

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 standardDeviation of x Source Edit

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

computes the sample standardDeviation 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: [].}

reset 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.

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: [].}

combine two RunningRegress objects.

Useful if performing parallel analysis of data series and need to re-combine parallel result sets

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

add RunningRegress b to a Source Edit