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@arki/math/stats

Inputs may be any iterable and are never mutated. Over plain numbers, sum uses compensated (Neumaier) summation, so sum([0.1, 0.2, 0.3]) is exactly 0.6. Give mean, median, minMax, variance or stddev an iterable of Decimal and you get an exact Decimal back (mean([decimal('0.1'), decimal('0.2')]) is 0.15; a mean that does not terminate needs { scale, rounding }, like division; stddev is correctly rounded at the scale you ask for). sum is number-only — Decimal.sum is the exact sum, and an empty list has no way to say which kind it wanted. variance/stddev default to the sample statistic (ddof: 1, like Python and Excel's STDEV); pass { ddof: 0 } for population. percentile(values, p) takes p in 0–100 and uses R‑7 linear interpolation (Excel PERCENTILE.INC, numpy's default). Empty input throws EmptyDataError; a non-finite element throws InvalidArgumentError.

import {
  linearRegression,
  mean,
  median,
  percentile,
  percentileRank,
  quantile,
  quartiles,
  stddev,
} from '@arki/math/stats';
 
mean([1, 2, 3, 4]); // 2.5
median([3, 1, 2]); // 2
percentile([1, 2, 3, 4], 25); // 1.75   p on 0–100
quantile([1, 2, 3, 4], 0.25); // 1.75   same thing, q on 0–1
quantile([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 0.25, { method: 'weibull' }); // 2.75   Excel PERCENTILE.EXC
quartiles([1, 2, 3, 4, 5, 6, 7, 8], { method: 'tukey' }); // { q1: 2.5, q2: 4.5, q3: 6.5 }   box-plot hinges
percentileRank([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 7); // 65
stddev([2, 4, 4, 4, 5, 5, 7, 9], { ddof: 0 }); // 2
linearRegression([1, 2, 3], [2, 4, 6]).slope; // 2

quantile and percentile take { method } for all nine Hyndman–Fan definitions (R types 1–9, named as in NumPy: 'inverseCdf' is nearest rank, 'weibull' is Excel PERCENTILE.EXC, 'linear' the default). quartiles adds two hinge rules for odd counts: 'tukey' keeps the median in both halves (R fivenum), 'medianExcluded' leaves it out (TI-83, Moore & McCabe). pooledVariance/pooledStddev combine groups, given as raw samples or as { n, stddev } / { n, variance } summaries. polynomialRegression centers x before solving, so year-scale x (2015…2024) fits; predict evaluates in the centered basis, because the power-basis coefficients lose digits there. The linear fit also reports adjustedR2, residualStandardError and the slope/intercept standard errors; these are undefined when no degrees of freedom are left (a line through two points).

Inference uses exact critical values from distributions (Student t by default, method: 'z' for the normal). sampleSize rounds up.

import { confidenceInterval, polynomialRegression, sampleSize, zScore } from '@arki/math/stats';
 
confidenceInterval([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]); // { mean: 5.5, lower: 3.33…, upper: 7.67…, … }  R t.test
sampleSize({ marginOfError: 0.03 }); // 1068   a ±3% poll at 95%
zScore(130, 100, 15); // 2
polynomialRegression([0, 1, 2, 3], [1, 2, 5, 10], 2).coefficients; // [1, 0, 1]  lowest degree first

Every fit (linearRegression, exponentialRegression, logarithmicRegression, powerRegression, polynomialRegression) returns its coefficients, r2 and predict(x). r2 is measured on the original y values, also for the fits that are solved on ln y.