[RFC]: Statistical Distribution Operations

[MutantPiggieGolem1]

Description

This RFC proposes the addition of operations (e.g. sum, difference, random sample) for statistical distributions (namely, the normal distribution. I am not versed in statistics and am not aware of the validity of operations for other distributions). It would also help to have a fitting function (constructor or static method) to determine parameters and create the distribution from a dataset. All of these are very common uses of a statistics library and would avoid the issue of needing to reimplement each function separately.

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Questions

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Checklist

• I have read and understood the Code of Conduct.
• Searched for existing issues and pull requests.
• The issue name begins with RFC:.

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[kgryte]

@MutantPiggieGolem1 How is what you are asking different from what is in https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dists/normal?

[MutantPiggieGolem1]

There are no functions to add two distributions, nor to take the difference between two, sample from them, or create one based on a dataset.

[kgryte]

For sampling, see https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/random/base/normal.

I am not sure what you mean by taking the difference between distributions. As for fitting, that is something we can add, but you'd need to make a much more concrete proposal for how that should be implemented.

[MutantPiggieGolem1]

For my use case, I've simply been computing the average and standard deviation of my arrays and using those as the distribution parameters.

Here is fitting:

export function std(x: number[]) {
  return stdev(x.length, 1, x, 1) || Number.EPSILON; // std cannot be 0, or things get unhappy.
}
export function avg(x: number[]) {
  return x.length === 0 ? 0 : x.reduce((a, b) => a + b, 0) / x.length;
}
export function fitNormal(x: number[]) {
  return new stats.Normal(avg(x), std(x));
}

Here is the difference:

export function normalDifference(
  minuend: Normal,
  subtrahend: Normal,
) {
  return new stats.Normal(
    minuend.mean - subtrahend.mean,
    Math.sqrt(minuend.stdev * minuend.stdev + subtrahend.stdev * subtrahend.stdev),
  );
}