Basic Distributions

/**
 * Returns a function for generating uniform distribution random numbers
 * @param min - Minimum value (inclusive), defaults to 0
 * @param max - Maximum value (exclusive), defaults to 1
 * @returns Generator function producing numbers in range [min, max)
 */
function randomUniform(min?: number, max?: number): () => number;

import { randomUniform } from "d3-random";

// Default range [0, 1)
const random01 = randomUniform();
console.log(random01()); // e.g., 0.7234

// Custom range [1, 6) - like a die roll
const die = randomUniform(1, 6);
console.log(Math.floor(die())); // 1, 2, 3, 4, or 5

// Single parameter sets max, min defaults to 0
const zeroToTen = randomUniform(10);
console.log(zeroToTen()); // e.g., 7.123

/**
 * Returns a function for generating uniform integer random numbers
 * @param min - Minimum integer value (inclusive), defaults to 0
 * @param max - Maximum integer value (exclusive)
 * @returns Generator function producing integers in range [⌊min⌋, ⌊max-1⌋]
 */
function randomInt(min?: number, max?: number): () => number;

import { randomInt } from "d3-random";

// Roll a six-sided die (1-6)
const die = randomInt(1, 7);
console.log(die()); // 1, 2, 3, 4, 5, or 6

// Random index for array of length 10
const arrayIndex = randomInt(10);
console.log(arrayIndex()); // 0, 1, 2, ..., or 9

// Random between -5 and 5
const centered = randomInt(-5, 6);
console.log(centered()); // -5, -4, ..., 4, or 5

/**
 * Returns a function for generating normal distribution random numbers
 * @param mu - Mean (expected value), defaults to 0
 * @param sigma - Standard deviation, defaults to 1
 * @returns Generator function producing normally distributed numbers
 */
function randomNormal(mu?: number, sigma?: number): () => number;

import { randomNormal } from "d3-random";

// Standard normal distribution (mean=0, stddev=1)
const standard = randomNormal();
console.log(standard()); // e.g., -0.234

// IQ scores (mean=100, stddev=15)
const iqScore = randomNormal(100, 15);
console.log(Math.round(iqScore())); // e.g., 103

// Height in inches (mean=68, stddev=4)
const height = randomNormal(68, 4);
console.log(height().toFixed(1)); // e.g., 71.2

/**
 * Returns a function for generating log-normal distribution random numbers
 * @param mu - Mean of the underlying normal distribution, defaults to 0
 * @param sigma - Standard deviation of the underlying normal distribution, defaults to 1
 * @returns Generator function producing log-normally distributed numbers
 */
function randomLogNormal(mu?: number, sigma?: number): () => number;

import { randomLogNormal } from "d3-random";

// Stock price movements
const stockPrice = randomLogNormal(0, 0.2);
console.log(stockPrice().toFixed(2)); // e.g., 1.15

// File sizes or network latencies
const fileSize = randomLogNormal(10, 1);
console.log(Math.round(fileSize())); // e.g., 18234

/**
 * Returns a function for generating exponential distribution random numbers
 * @param lambda - Rate parameter (1/mean)
 * @returns Generator function producing exponentially distributed numbers
 */
function randomExponential(lambda: number): () => number;

import { randomExponential } from "d3-random";

// Time between customer arrivals (average 1 every 5 minutes)
const customerArrival = randomExponential(1/5);
console.log(customerArrival().toFixed(1)); // e.g., 3.2 minutes

// Server response times (average 100ms)
const responseTime = randomExponential(1/100);
console.log(Math.round(responseTime())); // e.g., 85 ms

/**
 * Returns a function for generating Bates distribution random numbers
 * @param n - Number of independent uniform variables to average
 * @returns Generator function producing Bates distributed numbers
 */
function randomBates(n: number): () => number;

import { randomBates } from "d3-random";

// Approximate normal distribution using 10 uniform variables
const approximateNormal = randomBates(10);
console.log(approximateNormal().toFixed(3)); // e.g., 0.523

// More concentrated around 0.5 than uniform
const concentrated = randomBates(5);
console.log(concentrated().toFixed(3)); // e.g., 0.487

/**
 * Returns a function for generating Irwin-Hall distribution random numbers
 * @param n - Number of independent uniform variables to sum
 * @returns Generator function producing Irwin-Hall distributed numbers
 */
function randomIrwinHall(n: number): () => number;

import { randomIrwinHall } from "d3-random";

// Sum of 3 uniform variables (range 0-3)
const sum3 = randomIrwinHall(3);
console.log(sum3().toFixed(2)); // e.g., 1.75

// Approximate normal shape with integer parameter
const shaped = randomIrwinHall(12);
console.log(shaped().toFixed(2)); // e.g., 6.23