MATLAB Examples for Random Number Generation

Generating different types of random numbers in MATLAB is straightforward. This article introduces three common methods for random number generation with practical implementation details.

Uniformly Distributed Random Numbers in [0,1] Interval The `rand` function generates uniformly distributed random numbers in the range [0,1]. This function returns a pseudorandom value drawn from a continuous uniform distribution, where all values in the specified range are equally probable. For matrix generation, use syntax like `rand(m,n)` to create an m-by-n matrix of random values. This is particularly useful in Monte Carlo simulations, sampling algorithms, and randomized testing scenarios.

Standard Normal Distribution N(0,1) Random Numbers The `randn` function produces random numbers from a standard normal distribution with mean 0 and standard deviation 1. The underlying algorithm generates values following a Gaussian distribution using transformation methods like the Ziggurat or Polar algorithm. Similar to `rand`, you can specify dimensions using `randn(m,n)` for matrix outputs. These random numbers are essential in statistical analysis, noise modeling, financial risk assessment, and signal processing applications.

General Normal Distribution N(a,b) Random Numbers To generate normally distributed random numbers with mean a and standard deviation b, apply linear transformation to standard normal variates. The mathematical implementation is: `a + b*randn()`, where scaling by b adjusts the spread and adding a shifts the center. This transformation preserves the normal distribution properties while modifying its parameters. For generating multiple values, use `a + b*randn(m,n)` to create an m-by-n matrix following N(a,b) distribution.

MATLAB provides flexible parameter control for random number generation, including dimension specification through size arguments and reproducibility management using `rng` function for seed control. The Random Number Generation (RNG) settings can be configured via `rng(seed)` for repeatable results or `rng('shuffle')` for time-dependent initialization. These techniques have broad applications in financial modeling, signal processing, machine learning algorithms, and scientific simulations.