Module stats 

Descriptive statistics with numerical stability guarantees.

All functions in this module handle edge cases explicitly and use numerically stable algorithms to avoid catastrophic cancellation.

Algorithms

• Mean: Kahan compensated summation for O(ε) error independent of n.
• Variance/StdDev: Welford’s online algorithm. Reference: Welford (1962), “Note on a Method for Calculating Corrected Sums of Squares and Products”, Technometrics 4(3).
• Quantile: R-7 linear interpolation (default in R, Python, Excel). Reference: Hyndman & Fan (1996), “Sample Quantiles in Statistical Packages”, The American Statistician 50(4).

Structs

WelfordAccumulator

Streaming accumulator for mean, variance, skewness, and kurtosis.

Functions

covariance

Computes the sample covariance between two datasets.

kahan_sum

Neumaier compensated summation for O(ε) error independent of n.

kurtosis

Computes Fisher’s excess kurtosis (G₂) with bias correction.

max

Returns the maximum value in the slice.

mean

Computes the arithmetic mean using Kahan compensated summation.

median

Computes the median of data without mutating the input.

min

Returns the minimum value in the slice.

population_std_dev

Computes the population standard deviation.

population_variance

Computes the population variance using Welford’s online algorithm.

quantile

Computes the p-th quantile using the R-7 linear interpolation method.

quantile_sorted

Computes the p-th quantile on pre-sorted data (R-7 method).

skewness

Computes Fisher’s adjusted sample skewness (G₁) with bias correction.

std_dev

Computes the sample standard deviation.

variance

Computes the sample variance using Welford’s online algorithm.