import { Quantity } from "../model/Quantity.js";
/**
 * The statistics a sample of measurements is described with.
 *
 * The centre and the scatter are taken from the median rather than from
 * the mean, because the departures a measurement over an edition looks
 * for are in the sample it is taken over. A mean and a standard
 * deviation would grow towards those departures until they no longer
 * stood out; a median and a median absolute deviation leave them out of
 * account.
 */
/**
 * The middle of a sample, the mean of the two middle values where it has an even number of them.
 * @internal
 */
export declare const medianOf: <U extends string>(values: readonly Quantity<U>[]) => Quantity<U> | undefined;
/**
 * Where a sample sits and how far it scatters.
 * @category Collation and alignment
 */
export interface Spread<U extends string> {
    /** How many measurements it was taken over. */
    n: number;
    /** The middle measurement. */
    median: Quantity<U>;
    /**
     * The scatter about the median, as the median absolute deviation
     * scaled to the standard deviation a normal sample of that scatter
     * would have. It is zero where more than half the sample sits at
     * one value, and no scatter can be read off such a sample.
     */
    sigma: Quantity<U>;
}
/**
 * Where the sample sits and how far it scatters, or nothing for an empty sample.
 * @internal
 */
export declare const spreadOf: <U extends string>(values: readonly Quantity<U>[]) => Spread<U> | undefined;
/**
 * How far the value lies from the centre of the spread, in units of its scatter.
 * @internal
 */
export declare const standardise: <U extends string>(value: Quantity<U>, spread: Spread<U>) => number;
/**
 * The share of a normal sample lying below `z` standard deviations.
 * @internal
 */
export declare const normalBelow: (z: number) => number;
/**
 * The share of a normal sample lying further than `z` standard deviations from its centre, on either side.
 * @internal
 */
export declare const normalBeyond: (z: number) => number;
/**
 * How many standard deviations out the given share of a normal sample
 * lies below, after Acklam's rational approximation, whose relative
 * error stays below 1.15e-9. The inverse of `normalBelow`.
 * @internal
 */
export declare const normalQuantile: (share: number) => number;
/**
 * How much heavier the tails of a standardised sample are than a normal
 * sample's. Zero for a normal shape, positive where more of the sample
 * lies far out than the curve allows.
 * @internal
 */
export declare const excessKurtosisOf: (standardised: readonly number[]) => number;
/**
 * How much of a sample lies beyond a given distance from its centre, against how much would under a normal curve.
 * @category Collation and alignment
 */
export interface Tail {
    /** The distance from the centre, in standard deviations. */
    beyond: number;
    /** How many of the sample lie further out than that. */
    observed: number;
    /** How many a normal sample of the same size would put there. */
    expected: number;
}
/**
 * What the sample puts beyond the given distance, against what a normal sample would.
 * @internal
 */
export declare const tailOf: (standardised: readonly number[], beyond: number) => Tail;
/**
 * A sample counted into bins of one width.
 * @category Collation and alignment
 */
export interface Histogram<U extends string> {
    /** The bounds of the bins, in order, one more of them than there are counts. */
    edges: Quantity<U>[];
    /** How many of the sample fall in each bin. */
    counts: number[];
}
/**
 * The sample counted into bins of the given width, laid out on
 * multiples of that width so that two histograms of one width share
 * their bounds. Nothing for an empty sample or a width of nothing.
 * @internal
 */
export declare const histogramOf: <U extends string>(values: readonly Quantity<U>[], binWidth: Quantity<U>) => Histogram<U> | undefined;