Advanced & Applied Topics · Simulation & Monte Carlo Methods

Simulation: Pseudorandom number generation

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Computational Statistics · Stochastic Modeling

Overview

Topics covered

  • Introduction
  • Numerical Simulation: Generation of Variables and Pseudorandom Numbers
  • Theoretical Foundations and Introduction to Randomness
  • True Randomness vs. Pseudorandomness
  • The Universal Independent Uniform Hypothesis
  • Linear and multiplicative congruent generators

Related concepts

Main connections

  • Calculus & differentiation
  • Linear algebra & matrices
  • Conditional probability & independence
  • Residual analysis & diagnostics
  • Permutation & exact tests
  • Normal (Gaussian) distribution

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

Xn+1=(a⋅Xn+c)(modm)
View LaTeX sourceX_{n+1} = (a \cdot X_n + c) \pmod m