function xkurtosis
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.

Examples

Normal-like distribution

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([1, 2, 3, 4, 5]), -1.3);

Heavy-tailed distribution

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([1, 2, 3, 10]), -0.7696000000000001);

Matrix excess kurtosis

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([[1, 2, 3], [4, 5, 6]]), [-1.5, -1.5]);

Parameters

x: array

Input array or matrix

optional
flag: 0 | 1

Normalization flag (0: bias correction, 1: simple). Default is 1

optional
dim: 0 | 1

Dimension along which to compute excess kurtosis. Default is 0

Return Type

number

Excess kurtosis values

Throws

When input is invalid

xkurtosis(
x: matrix,
flag?: 0 | 1,
dim?: 0 | 1,
): array

Excess kurtosis.

Calculates the excess kurtosis (kurtosis - 3) which measures the "tailedness" relative to a normal distribution. Zero excess kurtosis indicates normal-like tails.

Examples

Normal-like distribution

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([1, 2, 3, 4, 5]), -1.3);

Heavy-tailed distribution

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([1, 2, 3, 10]), -0.7696000000000001);

Matrix excess kurtosis

import { assertEquals } from "jsr:@std/assert";

assertEquals(xkurtosis([[1, 2, 3], [4, 5, 6]]), [-1.5, -1.5]);

Parameters

Input array or matrix

optional
flag: 0 | 1

Normalization flag (0: bias correction, 1: simple). Default is 1

optional
dim: 0 | 1

Dimension along which to compute excess kurtosis. Default is 0

Return Type

Excess kurtosis values

Throws

When input is invalid

Usage

import xkurtosis from "stats/xkurtosis.ts";