import type { array, matrix } from "../types";
/**
 * Excess kurtosis.
 *
 * Calculates the excess kurtosis (kurtosis - 3) which measures the "tailedness"
 * relative to a normal distribution. Zero excess kurtosis indicates normal-like tails.
 *
 * @param x Input array or matrix
 * @param flag Normalization flag (0: bias correction, 1: simple). Default is 1
 * @param dim Dimension along which to compute excess kurtosis. Default is 0
 * @returns Excess kurtosis values
 * @throws When input is invalid
 *
 * @example Normal-like distribution
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([1, 2, 3, 4, 5]), -1.3);
 *
 * ```
 *
 * @example Heavy-tailed distribution
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([1, 2, 3, 10]), -0.7696000000000001);
 *
 * ```
 *
 * @example Matrix excess kurtosis
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([[1, 2, 3], [4, 5, 6]]), [-1.5, -1.5]);
 * ```
 */
export default function xkurtosis(x: array, flag?: 0 | 1, dim?: 0 | 1): number;
/**
 * Excess kurtosis.
 *
 * Calculates the excess kurtosis (kurtosis - 3) which measures the "tailedness"
 * relative to a normal distribution. Zero excess kurtosis indicates normal-like tails.
 *
 * @param x Input array or matrix
 * @param flag Normalization flag (0: bias correction, 1: simple). Default is 1
 * @param dim Dimension along which to compute excess kurtosis. Default is 0
 * @returns Excess kurtosis values
 * @throws When input is invalid
 *
 * @example Normal-like distribution
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([1, 2, 3, 4, 5]), -1.3);
 *
 * ```
 *
 * @example Heavy-tailed distribution
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([1, 2, 3, 10]), -0.7696000000000001);
 *
 * ```
 *
 * @example Matrix excess kurtosis
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(xkurtosis([[1, 2, 3], [4, 5, 6]]), [-1.5, -1.5]);
 * ```
 */
export default function xkurtosis(x: matrix, flag?: 0 | 1, dim?: 0 | 1): array;
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