/**
 * Statistical kernel for the Explain Data module.
 *
 * FROZEN for the executor agent: do not modify scoring logic here.
 * See docs/explain-data-worklog.md §1.
 */
/**
 * Laplace-smooth a non-negative mass vector into a probability vector.
 * alpha adds pseudo-mass to every category so small samples do not
 * produce spuriously extreme distributions.
 */
export declare function laplaceSmooth(mass: number[], alpha?: number): number[];
/**
 * Jensen–Shannon divergence (base 2) between two aligned probability vectors.
 * Zero-probability categories contribute by definition (0·log0 = 0; the
 * non-zero side contributes 0.5·p). Bounded in [0, 1].
 */
export declare function jsDivergence(p: number[], q: number[]): number;
/**
 * Jensen–Shannon distance: sqrt of the divergence. A proper metric,
 * bounded in [0, 1] and comparable across candidate dimensions of
 * different cardinalities.
 */
export declare function jsDistance(p: number[], q: number[]): number;
/**
 * Element-wise `total − part`, clamped at 0 (guards float noise).
 * Used to derive the siblings distribution from the all-marks totals
 * without an extra query; valid for additive masses (counts, sums).
 */
export declare function subtractMass(total: number[], part: number[]): number[];
/** log Γ(x) via Lanczos approximation, x > 0. */
export declare function logGamma(x: number): number;
/**
 * Upper-tail probability of the chi-square distribution:
 * P(X ≥ x) for X ~ χ²(df).
 */
export declare function chiSquareUpperTail(x: number, df: number): number;
/**
 * G-test of goodness of fit: are the observed category counts consistent
 * with the expected probabilities?
 *
 * @param observed raw counts for the selected mark, aligned with expectedProbs
 * @param expectedProbs probability vector (e.g. smoothed sibling shares)
 * @returns p-value; small p ⇒ the mark's composition differs significantly
 */
export declare function gTestPValue(observed: number[], expectedProbs: number[]): number;