/Nim

Module stats

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()```

math

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
```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

Procs

`proc clear(s: var RunningStat) {...}{.raises: [], tags: [].}`
reset s
`proc push(s: var RunningStat; x: float) {...}{.raises: [], tags: [].}`
pushes a value x for processing
`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
`proc variance(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current population variance of s
`proc varianceS(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current sample variance of s
`proc standardDeviation(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current population standard deviation of s
`proc standardDeviationS(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current sample standard deviation of s
`proc skewness(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current population skewness of s
`proc skewnessS(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current sample skewness of s
`proc kurtosis(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current population kurtosis of s
`proc kurtosisS(s: RunningStat): float {...}{.raises: [], tags: [].}`
computes the current sample kurtosis of s
`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
`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
`proc variance[T](x: openArray[T]): float`
computes the population variance of x
`proc varianceS[T](x: openArray[T]): float`
computes the sample variance of x
`proc standardDeviation[T](x: openArray[T]): float`
computes the population standardDeviation of x
`proc standardDeviationS[T](x: openArray[T]): float`
computes the sanple standardDeviation of x
`proc skewness[T](x: openArray[T]): float`
computes the population skewness of x
`proc skewnessS[T](x: openArray[T]): float`
computes the sample skewness of x
`proc kurtosis[T](x: openArray[T]): float`
computes the population kurtosis of x
`proc kurtosisS[T](x: openArray[T]): float`
computes the sample kurtosis of x
`proc clear(r: var RunningRegress) {...}{.raises: [], tags: [].}`
reset r
`proc push(r: var RunningRegress; x, y: float) {...}{.raises: [], tags: [].}`
pushes two values x and y for processing
`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.
`proc slope(r: RunningRegress): float {...}{.raises: [], tags: [].}`
computes the current slope of r
`proc intercept(r: RunningRegress): float {...}{.raises: [], tags: [].}`
computes the current intercept of r
`proc correlation(r: RunningRegress): float {...}{.raises: [], tags: [].}`
computes the current correlation of the two data sets pushed into r
`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: [].}`