type Vec = readonly number[] | Float64Array;
/**
 * Ranks of the data with tie handling (SciPy `rankdata`, default `'average'`):
 * tied values receive the mean of the ranks they span. Ranks are 1-based.
 */
export declare function rankdata(x: Vec): number[];
/**
 * Spearman rank correlation coefficient ρ — the Pearson correlation of the
 * rank-transformed inputs (ties broken by average ranks via {@link rankdata}).
 * Unlike Pearson, it measures any MONOTONIC relationship, so a monotonic
 * non-linear pair (e.g. `y = x²` on positives) gives ρ = 1. Result is in [−1, 1].
 *
 * @throws if the inputs differ in length or a rank vector is constant.
 */
export declare function spearman(x: Vec, y: Vec): number;
/** Geometric mean: `exp(mean(ln x))` (stable form). All entries must be > 0. */
export declare function gmean(x: Vec): number;
/** Harmonic mean: `n / Σ(1/xᵢ)`. All entries must be > 0. */
export declare function hmean(x: Vec): number;
/** Raw or central k-th moment. `central` (default true) subtracts the mean first. */
export declare function moment(x: Vec, k: number, central?: boolean): number;
/**
 * Skewness (third standardized moment). Population estimator by default
 * (SciPy `bias=true`); pass `{ bias: false }` for the sample-corrected G₁.
 */
export declare function skewness(x: Vec, opts?: {
    bias?: boolean;
}): number;
/**
 * Kurtosis. Excess kurtosis by default (SciPy `fisher=true`, subtracts 3);
 * pass `{ fisher: false }` for Pearson's kurtosis. Population estimator by
 * default; `{ bias: false }` applies the sample correction.
 */
export declare function kurtosis(x: Vec, opts?: {
    fisher?: boolean;
    bias?: boolean;
}): number;
/** Interquartile range: `Q3 − Q1` via `quantileSeq`. */
export declare function iqr(x: Vec): number;
/** Standard error of the mean: `sampleStd / √n`. */
export declare function sem(x: Vec): number;
/**
 * Z-scores: `(xᵢ − mean) / std`, using population std (SciPy `zscore` default,
 * `ddof=0`). Returns an array the same length as the input.
 */
export declare function zscore(x: Vec): number[];
/**
 * Covariance.
 *   - `cov(x, y)` → scalar sample covariance of two equal-length vectors.
 *   - `cov(matrix)` → covariance matrix; rows are observations, columns are
 *     variables (NumPy `rowvar=false`). `ddof` defaults to 1 (sample).
 */
export declare function cov(x: Vec | number[][], y?: Vec, ddof?: number): number | number[][];
/**
 * Correlation-coefficient matrix from {@link cov} (rows = observations,
 * columns = variables). Diagonal is 1; off-diagonals are Pearson r.
 */
export declare function corrcoef(matrix: number[][]): number[][];
/**
 * Kendall's τ_b rank correlation coefficient — a tie-corrected measure of
 * ordinal association based on the difference between concordant and discordant
 * pairs. Complements {@link spearman} (rank Pearson) and Pearson `corr`.
 * Returns τ_b = (P − Q) / √((n₀ − n₁)(n₀ − n₂)), matching `scipy.stats.kendalltau`
 * (`variant='b'`, its default), where n₀ = n(n−1)/2 and n₁/n₂ are the tie-pair
 * counts in x and y respectively.
 *
 * @example kendallTau([1,2,3,4,5], [2,1,4,3,5]) // 0.6
 */
export declare function kendallTau(x: Vec, y: Vec): number;
/** Result of a simple linear regression with inference. */
export interface LinRegressResult {
    slope: number;
    intercept: number;
    rValue: number;
    pValue: number;
    stdErr: number;
    interceptStdErr: number;
}
/**
 * OLS simple linear regression **with inference** — `y ≈ slope·x + intercept`,
 * plus the correlation coefficient, the slope p-value (t-test, df = n−2), and
 * the slope/intercept standard errors. Matches `scipy.stats.linregress`.
 */
export declare function linregress(x: Vec, y: Vec): LinRegressResult;
/** A correlation coefficient with its two-tailed significance p-value. */
export interface CorrelationTestResult {
    coefficient: number;
    pValue: number;
}
/** Pearson correlation **test** (coefficient + two-tailed p, t-test). `scipy.stats.pearsonr`. */
export declare function pearsonr(x: Vec, y: Vec): CorrelationTestResult;
/** Spearman rank-correlation **test** (rho + two-tailed p, t-test). `scipy.stats.spearmanr`. */
export declare function spearmanr(x: Vec, y: Vec): CorrelationTestResult;
/**
 * Kendall's τ **test** — τ_b coefficient and two-tailed p via the normal
 * approximation `z = 3τ√(n(n−1)) / √(2(2n+5))` (standard large-sample form;
 * scipy's small-n exact p is version/table-specific).
 */
export declare function kendalltau(x: Vec, y: Vec): CorrelationTestResult;
/** Result of {@link kendallTauTest}: the τ_b coefficient plus its p-value. */
export interface KendallTauTestResult {
    tau: number;
    pValue: number;
}
/**
 * Kendall's τ **test** (hypothesis-test naming convenience) — identical to
 * {@link kendalltau} (τ_b coefficient + two-tailed normal-approximation
 * p-value), just returning `{ tau, pValue }` instead of `{ coefficient,
 * pValue }` to match the `*Test` result-object convention used by
 * `mannWhitneyTest`/`kolmogorovSmirnovTest`/etc. Does not duplicate the
 * coefficient/p-value logic — delegates to `kendalltau`.
 *
 * @example kendallTauTest([1,2,3,4,5], [1,2,3,4,5]) // { tau: 1, pValue: <small> }
 */
export declare function kendallTauTest(x: Vec, y: Vec): KendallTauTestResult;
/** Peak-to-peak / statistical range: max − min. (`np.ptp`; `range` is taken.) */
export declare function ptp(x: Vec): number;
/** Coefficient of variation: population-std / mean (`scipy.stats.variation`, ddof=0). */
export declare function variation(x: Vec): number;
/** Trimmed mean — drop `proportion` of the sorted data from each tail. `scipy.stats.trim_mean`. */
export declare function trimmedMean(x: Vec, proportion: number): number;
/** Summary statistics bundle (`scipy.stats.describe`): sample variance (ddof=1); biased Fisher skew/kurtosis. */
export interface DescribeResult {
    nobs: number;
    min: number;
    max: number;
    mean: number;
    variance: number;
    skewness: number;
    kurtosis: number;
}
/**
 * Return summary statistics of `x`, as `scipy.stats.describe` does.
 *
 * The variance is the sample variance (ddof = 1). The skewness and the excess kurtosis are
 * the biased estimates.
 *
 * @throws Error if `x` is empty.
 */
export declare function describe(x: Vec): DescribeResult;
/** Histogram counts and bin edges (`np.histogram`) — `bins` equal-width bins over [min, max]. */
export interface HistogramResult {
    counts: number[];
    edges: number[];
}
/**
 * Count the values of `x` in `bins` equal-width bins from the minimum to the maximum.
 *
 * The last bin includes the maximum. If all values are equal, the range is that value
 * plus and minus 0.5.
 *
 * @throws Error if `x` is empty, or if `bins` is not a positive integer.
 */
export declare function histogram(x: Vec, bins?: number): HistogramResult;
export {};
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