Descriptive statistics, correlation, tests, and fitting over tensors and frame columns.

Import with use math.stats. Functions become top-level after import.

Function	Description	Example
`median[x]`	Median of a 1D array	Statistics: `use math.stats`
`std[x]`	Population standard deviation	Statistics: `use math.stats`
`var[x]`	Population variance	Statistics: `use math.stats`
`percentile[x, p]`	p-th percentile (0-100) with linear interpolation	Statistics: `use math.stats`
`zscore[x]`	Z-score normalization: (x - mean) / std → returns array	Statistics: `use math.stats`
`corr[x, y]`	Pearson correlation coefficient between two arrays	Statistics: `use math.stats`
`cov[x, y]`	Population covariance between two arrays	Statistics: `use math.stats`
`ttest[x, y]`	Welch's two-sample t-test → returns map with `t` and `p`	Statistics: `use math.stats`
`linreg[x, y]`	Simple linear regression → returns map with `slope`, `intercept`, `r2`	Statistics: `use math.stats`
`chisq[observed, expected]`	Chi-square goodness-of-fit test → map with `chi2`, `p`	Statistics: `use math.stats`
`anova[g1, g2, ...]`	One-way ANOVA → map with `f`, `p`	Statistics: `use math.stats`
`kstest[data, dist_name]`	Kolmogorov-Smirnov test → map with `d`, `p`. Distributions: `"normal"`, `"uniform"`	Statistics: `use math.stats`
`fit[data, dist_name]`	Distribution fitting (MLE) → map of parameters. Distributions: `"normal"` → `{mu, sigma}`, `"exponential"` → `{lambda}`, `"uniform"` → `{a, b}`, `"poisson"` → `{lambda}`	Statistics: `use math.stats`

A statistic of no values is NaN. The series a function pairs up (corr, cov, linreg, chisq) are one length, percentile's p is from 0 to 100, anova compares two groups or more, and kstest and fit know the distributions above; anything else stops the program with the reason (see When a Program Stops). They had answered NaN, 0.5 or an empty map.

The module is written in Crow (src/modules/stats.co, design rule 20): each statistic is a formula over the math builtins — a median the middle of sort, a variance the mean of squared distances, a regression its sums of products — and the tests' p-values are the t, F and chi-square distributions written over the sys layer's betainc and gammainc, which stay validated kernels. Its rows keep the contract above in both modes; its tests are the module's own (crow test src/modules/stats.co): each statistic at known values, and its laws over a spread of inputs (a median is the 50th percentile, a series' covariance with itself is its variance, a correlation is symmetric and within −1 and 1, a z-score keeps nothing of the scale, a line through its own points has r² 1).

use math
use math.stats

x = linspace[1, 10, 10]
log[median[x]]            --- 5.5
log[std[x]]               --- 2.872...
log[var[x]]               --- 8.25
log[percentile[x, 25]]    --- 3.25

z = zscore[x]             --- mean=0, std=1

y = linspace[2, 20, 10]
log[corr[x, y]]           --- 1.0 (perfect correlation)
log[cov[x, y]]            --- 16.5

result = ttest[x, y]
log[result.t]                   --- t-statistic
log[result.p]                   --- p-value

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