Stats

Pearson correlation coefficient. Returns value in [-1, 1]. Panics if lists have different lengths, fewer than 2 elements, or if either list has zero standard deviation.

The two *structural* preconditions are declared in the signature (`xs` has at
least 2 elements; `ys` has exactly as many as `xs`), so a provable violation
of either is a compile error. The zero-standard-deviation panic is
data-dependent — it turns on the `Float` *values* in the lists, not on their
shape — so no measure can express it and it stays a runtime check.

Number of elements.

Sample covariance of two equal-length lists. Panics if lengths differ or if either list has fewer than 2 elements.

Both structural preconditions are declared in the signature — `xs` must have
at least 2 elements and `ys` must have exactly as many as `xs` — so a call the
compiler can prove violates either is a compile error rather than a runtime
panic. Lengths it cannot relate are accepted in silence (March reports only
definite failures) and the `panic`s below remain the runtime backstop.

Five-number summary with selectable method: (min, Q1, median, Q3, max). Panics on empty list.

Interquartile range: Q3 − Q1 using the given method.

Uses the same sorted list for both quartiles (one sort, not two).
Panics on empty input.

Interquartile range using Linear (Type 7) interpolation.

Simple linear regression: y = slope * x + intercept. Returns (slope, intercept). Panics if lists have different lengths or fewer than 2 elements, or if xs has zero variance (vertical line).

The two *structural* preconditions are declared in the signature (`xs` has at
least 2 points; `ys` has exactly as many as `xs`), so a provable violation of
either is a compile error. The zero-variance panic is data-dependent — it
turns on the `Float` *values* in `xs`, not on their shape — so no measure can
express it and it stays a runtime check.

Maximum value, returning Err on empty list.

Maximum value. Panics on empty list.

Arithmetic mean. Panics on empty list.

Mean, returning Err on empty list instead of panicking.

Median (50th percentile). Panics on empty list.

Minimum value, returning Err on empty list.

Minimum value. Panics on empty list.

Mode: the most frequently occurring value. When there are ties, returns the first value encountered (in sorted order). Panics on empty list.

Percentile using linear interpolation. p must be in [0.0, 100.0]. Panics on empty list or out-of-range p.

Quantile at probability q ∈ [0.0, 1.0] using the given interpolation method. Panics on empty list or out-of-range q.

For a percentile-style API (q in 0..100), see `percentile`.  The
existing `percentile(xs, p)` is equivalent to
`quantile(xs, p / 100.0, Linear)`.

Quantile with Linear interpolation (Type 7, R/numpy default). Convenience alias for quantile(xs, q, Linear).

Batched quantiles: returns [quantile(xs, q, method) for q in qs]. Sorts the input once and reuses it for each q.

Sample standard deviation. Returns 0.0 for single element. Panics on empty.

Population standard deviation.

Sample standard deviation, returning Err on empty or single-element list.

Sum of all elements. Returns 0.0 for empty list.

Sample variance (denominator n-1). Returns 0.0 for a single element. Panics on empty list.

Uses Welford's online algorithm for numerical stability on inputs
where the naive two-pass sum-of-squares would suffer catastrophic
cancellation (near-constant data, shifted distributions).

Population variance (denominator n). Returns 0.0 for a single element or empty list.

Uses Welford's online algorithm (same stability benefit as `variance`).

Sample variance, returning Err on empty list.