atlas-dataset

Calculate mean, standard deviation, sum for a set of data points.

install

npm install --save atlas-dataset

why

A minimal wrapper, allowing for basic statistical inspection of an array of numbers. All linear and polylogarithmic calculations are cached on-demand and reused.

examples

instantiate a new Dataset

For these examples, we'll be using an array of 1,000,000 random floats between zero and one. When you instantiate a new Dataset, the array is shallow copied to avoid manipulating the original:

const Dataset = require("atlas-dataset");
const arr = [];
for (let i = 1e6; i--;){
  arr.push(Math.random())
}
const set = new Dataset(arr)

calculate values

...
console.log(`size: ${set.size()} sum: ${set.sum()}`)
console.log(`value: ${set.mean()} +/- ${set.stddev()}`)
console.log(`median: ${set.median()} +/- ${set.mad()}`)
// size: 1000000 sum: 500128.4297823687
// mean: 0.5001284297823687 +/- 0.2884814684388095
// median: 0.4996962409854201 +/- 0.24966274565483493

updating the data

...
set.add(Math.random());
console.log(`size: ${set.size()} sum: ${set.sum()}`)
console.log(`value: ${set.mean()} +/- ${set.stddev()}`)
console.log(`median: ${set.median()} +/- ${set.mad()}`)
// size: 1000001 sum: 500128.76868722256
// mean: 0.500128268558954 +/- 0.2884813692496768
// median: 0.4996961275123013 +/- 0.2496624248162307

caveats

In the examples, arr is not normally distributed, nor are we caring about the amount of significant figures in the result.

todo

For efficiently updating calculations, derive a recurrence relation for each quantity, V:

V(X_n+1) = f(V(X_n), x_n+1)

For example Mu_n+1 = (Mu_n*n + x_n+1)/(n+1) and updating the size and sum is trivial. Recomputing stddev is easy using the forumla: s^2 = <x^2> - <x>^2. Just square s_n, compute s_n+1^2 then take the square root. Updating the mean square is the exact same thing as updating the mean, we just replace x_n+1 with x_n+1^2 in the numerator.