Descriptive statistics

The Nautilus.Stats module provides descriptive statistics over tensor[n, f32] vectors. All functions are polymorphic over the tensor length n and return f32 scalars.

Central tendency

Function	Signature	Notes
`mean_vec`	`[n](v: tensor[n, f32]) -> f32`	Arithmetic mean
`median_vec`	`[n](v: tensor[n, f32]) -> f32`	Sorts internally; averages middle two for even n
`trimmed_mean_vec`	`[n](v: tensor[n, f32], proportion: f32) -> f32`	Trims `proportion` from each tail; NaN if proportion >= 0.5

Dispersion

Function	Signature	Notes
`variance_vec`	`[n](v: tensor[n, f32], ddof: int64) -> f32`	ddof=0 for population, ddof=1 for sample
`std_vec`	`[n](v: tensor[n, f32], ddof: int64) -> f32`	sqrt(variance_vec)
`range_vec`	`[n](v: tensor[n, f32]) -> f32`	max - min

Shape

Function	Signature	Notes
`skewness_vec`	`[n](v: tensor[n, f32]) -> f32`	Population skewness (biased, not adjusted)
`kurtosis_vec`	`[n](v: tensor[n, f32]) -> f32`	Excess kurtosis (Fisher convention, subtracts 3)

Order statistics

Function	Signature	Notes
`min_vec`	`[n](v: tensor[n, f32]) -> f32`
`max_vec`	`[n](v: tensor[n, f32]) -> f32`
`quantile_vec`	`[n](v: tensor[n, f32], q: f32) -> f32`	q in [0,1], linear interpolation, sorts internally
`percentile_vec`	`[n](v: tensor[n, f32], p: f32) -> f32`	p in [0,100], delegates to quantile_vec

Two-sample

Function	Signature	Notes
`covariance_scalar`	`[n](a: tensor[n, f32], b: tensor[n, f32], ddof: int64) -> f32`	Scalar covariance between two vectors
`correlation_scalar`	`[n](a: tensor[n, f32], b: tensor[n, f32]) -> f32`	Pearson r (uses ddof=0 internally)

Example

module Nautilus.BookStatsSummary
import Nautilus.Stats (mean_vec, variance_vec, median_vec)
export (summary)
def summary[n](data: tensor[n, f32]) -> (f32, f32, f32) = {
  mu = mean_vec(copy(data))
  v = variance_vec(copy(data), cast(1, int64))
  med = median_vec(data)
  (mu, v, med)
}

Notes

Use copy(data) when passing the same tensor to multiple statistics functions (linear-use discipline).
skewness_vec and kurtosis_vec use population (biased) moments, matching the default behavior of scipy.stats.skew/kurtosis with bias=True.
quantile_vec clamps q to [0, 1] and uses linear interpolation between adjacent sorted values.
trimmed_mean_vec truncates (floor) the trim count, so small proportions on short vectors may trim nothing.