The GSL-RUNNING-STATISTICS module

The gsl-running-statistics module provides routines for computing running statistics. These routines process data in a single pass, making them suitable for large datasets where storing all points in memory is impractical. The module supports exact calculations for mean, variance, and higher-order moments, as well as approximate calculations for medians and quantiles.

Statistical summary

Here is a basic example of how to use the statistical functions:

let data = #[17.2d0, 18.1d0, 16.5d0, 18.3d0, 12.6d0];

let rstat = make(<rstat>);

// for (x in data) rstat-add!(rstat, x) end
rstat-add!(rstat, data);

format-out("The dataset is %=\n", data);

format-out("The sample mean is %=\n", rstat.rstat-mean);
format-out("The estimated variance is %=\n", rstat.rstat-variance);
format-out("The largest value is %=\n", rstat.rstat-max);
format-out("The smallest value is %=\n", rstat.rstat-min);
format-out("The median is %=\n", rstat.rstat-median);
format-out("The standard deviation is %=\n", rstat.rstat-sd);
format-out("The root mean square is %=\n", rstat.rstat-rms);
format-out("The standard devation of the mean is %=\n", rstat.rstat-sd-mean);
format-out("The skew is %=\n", rstat.rstat-skew);
format-out("The kurtosis %=\n", rstat.rstat-kurtosis);
format-out("There are %d items in the accumulator\n", rstat.rstat-n);

rstat.rstat-reset!;
format-out("There are %d items in the accumulator\n", rstat.size);

Class and current statistics

<rstat> Class
Superclasses:

<object>

Slots:

  • rstat-min – An instance of <double-float>. Minimal value seen so far.

  • rstat-max – An instance of <double-float>. Maximal value seen so far.

  • rstat-mean – An instance of <double-float>. Mean of the values seen so far.

  • rstat-variance – An instance of <double-float>. Variance of the values seen so far.

  • rstat-sd – An instance of <double-float>. Standard deviation of the values seen so far.

  • rstat-sd-mean – An instance of <double-float>. Standard deviation of the mean of the values seen so far.

  • rstat-rms – An instance of <double-float>. Root mean square of the values seen so far.

  • rstat-skew – An instance of <double-float>. Skewness of the values seen so far.

  • rstat-kurtosis – An instance of <double-float>. Kurtosis of the values seen so far.

  • rstat-median – An instance of <double-float>. Median of the values seen so far.

  • rstat-norm – An instance of <double-float>. Norm of the values seen so far.

size(<rstat>) Method
Signature:

size (rstat) => (n :: <integer>)

Parameters:

  • rstat – An instance of <rstat>.

Adding values to the accumulator

rstat-add! Generic function
Signature:

rstat-add! (rstat, x) => ()

Parameters:
rstat-add!(<double-float>) Method
Signature:

rstat-add! (rstat, x) => ()

Parameters:

  • rstat – An instance of <rstat>.

  • x – A <double-float>.

rstat-add!(<sequence>) Method
Signature:

rstat-add! (rstat, x) => ()

Parameters:

Resetting the accumulator

rstat-reset! Function
Signature:

rstat-reset! (rstat) => ()

Parameters:

  • rstat – An instance of <rstat>.

Quantiles

<quantile-rstat> Class
Superclasses:

<object>

Slots:

  • quantile-rstat-p – An instance of <double-float>. The probability of the quantile.

quantile-rstat-add! Generic function
Signature:

quantile-rstat-add! (quantile-rstat, x) => ()

Parameters:
quantile-rstat-add!(<double-float>) Method
Signature:

quantile-rstat-add! (quantile-rstat, x) => ()

Parameters:
quantile-rstat-add!(<sequence>) Method
Signature:

quantile-rstat-add! (quantile-rstat, x) => ()

Parameters:
quantile-rstat-get Function
Signature:

quantile-rstat-get (quantile-rstat) => (quantile :: <double-float>)

Parameters:
quantile-rstat-reset! Function
Signature:

quantile-rstat-reset! (quantile-rstat) => ()

Parameters: