Module stats 

Descriptive and inferential statistics functions. Descriptive statistics — population & sample variance, sd, se, median, quantile, IQR, skewness, kurtosis, z-score, standardize.

Determinism Contract

• Unordered reductions use BinnedAccumulatorF64 for order-invariant, bit-identical results regardless of input order.
• Cumulative (ordered) operations use KahanAccumulatorF64 where the addition order IS the semantics.
• Sorting uses f64::total_cmp for deterministic NaN handling.
• No HashMap, no par_iter, no OS randomness.
• Same input => bit-identical output.

Functions

cor

Pearson correlation coefficient between two arrays. cor(x, y) = cov(x,y) / (sd(x) * sd(y))

cor_ci

Confidence interval for Pearson correlation using Fisher z-transform. Returns (lower_bound, upper_bound).

cor_matrix

Correlation matrix for a set of variables (columns). Returns flat Vec of n x n correlation matrix.

cov

Population covariance: sum((xi-mx)(yi-my)) / n.

cov_matrix

Covariance matrix. Returns flat Vec of n x n covariance matrix.

cume_dist

Cumulative distribution: count(x_i <= x_j) / n for each x_j.

cummax

Cumulative max.

cummin

Cumulative min.

cumprod

Cumulative product.

cumsum

Cumulative sum with Kahan summation.

dense_rank

Dense rank (no gaps for ties). Returns 1-based ranks.

filter_mask

Boolean mask selection: return elements of data where mask is true.

histogram

Histogram: bin data into n equal-width bins. Returns (bin_edges: Vec, counts: Vec).

iqr

Interquartile range: Q3 - Q1.

kendall_cor

Kendall tau-b correlation coefficient with tie adjustment. O(n^2) pairwise comparison for determinism.

kurtosis

Kurtosis (excess kurtosis, Fisher’s): E[(X-mu)^4] / sigma^4 - 3.

lag

Lag: shift values forward by n positions, fill with NaN.

lead

Lead: shift values backward by n positions, fill with NaN.

mad

Median absolute deviation: median(|x[i] - median(x)|). Does NOT multiply by 1.4826 scaling factor.

median

Median: middle value of sorted data. For even n, average of two middle values. Clones and sorts internally — never mutates input.

median_fast

O(n) median using introselect instead of O(n log n) sort. For even n, selects both middle elements via two partial sorts.

mode

Mode: most frequent value. Ties broken by smallest value. Uses bit-exact comparison via to_bits() on a sorted copy.

n_distinct

Number of distinct values in the data. Uses sorted unique comparison for determinism (no HashMap).

nth_element

Introselect: partition-based O(n) expected selection of the k-th smallest element. Operates on a mutable slice and partially reorders it so that data[k] holds the k-th smallest value (0-indexed), all elements data[..k] are <= data[k], and all data[k+1..] are >= data[k].

nth_element_copy

Non-mutating nth_element: clones data, selects k-th element, returns it. O(n) expected time, O(n) space for the clone.

ntile

Divide data into n roughly equal groups (ntile/quantile binning). Returns 1-based group assignments matching original data order.

partial_cor

Partial correlation: correlation of x and y controlling for z.

percent_rank_fn

Percent rank: (rank - 1) / (n - 1), range [0, 1]. Uses average-tie ranking from existing rank() function.

percentile_rank

Percentile rank: fraction of data values strictly less than the given value, plus half the fraction equal to the value. Returns a value in [0, 1].

pop_sd

Population standard deviation: sqrt(pop_variance).

pop_variance

Population variance: sum((xi - mean)^2) / N.

quantile

Quantile at probability p (0.0 to 1.0). Linear interpolation between adjacent ranks (R type 7 / NumPy default).

quantile_fast

O(n) quantile using introselect (R type 7 interpolation).

rank

Rank (average ties). Returns 1-based ranks. DETERMINISM: uses stable sort with index tracking.

row_number

Row number (sequential, tie-broken by original position — stable).

sample_cov

Sample covariance: sum((xi-mx)(yi-my)) / (n-1).

sample_indices

Generate k random indices in [0, n) with or without replacement.

sample_sd

Sample standard deviation: alias for sd() (both use N-1 denominator).

sample_variance

Sample variance: alias for variance() (both use N-1 denominator).

sd

Standard deviation (sample, N-1 denominator — R/pandas default).

se

Standard error of the mean: sample_sd / sqrt(n).

skewness

Skewness (Fisher’s definition): E[(X-mu)^3] / sigma^3.

spearman_cor

Spearman rank correlation: Pearson correlation of the ranks of x and y.

standardize

Min-max normalization: (xi - min) / (max - min).

trimmed_mean

Trimmed mean: mean of data with proportion fraction removed from each tail. proportion=0.1 removes bottom 10% and top 10%, computing mean of middle 80%.

variance

Variance (sample, N-1 denominator — R/pandas default). Two-pass: first binned mean, then binned sum of squared deviations. For single element, returns 0.

weighted_mean

Weighted mean: sum(data[i] * weights[i]) / sum(weights). Uses binned accumulation for both numerator and denominator.

weighted_var

Weighted variance: sum(w[i] * (x[i] - weighted_mean)^2) / sum(w). Two-pass: first weighted mean (binned), then binned sum of squared deviations.

winsorize

Winsorize: replace values below the proportion quantile with the lower boundary, and values above the (1-proportion) quantile with the upper boundary.

z_score

Z-scores: (xi - mean) / sd for each element.