Creating Gaussian random variable with MATLAB

Question

By using randn function I want to create a Gaussian random variable X such that X ~ N(2,4) and plot this simulated PDF together with theoretic curve.

Possible duplicate of [Draw Normal Distribution Graph of a Sample in Matlab](https://stackoverflow.com/questions/11831690/draw-normal-distribution-graph-of-a-sample-in-matlab) — SecretAgentMan, Jul 08 '19 at 14:49
Also see [this answer's code](https://stackoverflow.com/a/52902148/8239061) which has an example to both generate samples to estimate the PDF and compare with the theoretical PDF. You can also repeat [this example](https://stackoverflow.com/a/53876868/8239061) but leave off the *truncation*. — SecretAgentMan, Jul 08 '19 at 14:56
Possible duplicate of [Random Numbers with Gaussian and Uniform Distributions in matlab](https://stackoverflow.com/q/13844944/8239061) — SecretAgentMan, Jul 08 '19 at 14:57

score 7 · Answer 1 · answered Oct 27 '12 at 14:44

Matlab randn generates realisations from a normal distribution with zero mean and a standard deviation of 1. Samples from any other normal distribution can simply be generated via:

numSamples = 1000;
mu = 2;
sigma = 4;
samples = mu + sigma.*randn(numSamples, 1);

You can verify this by plotting the histogram:

figure;hist(samples(:));

See the matlab help.

score 3 · Answer 2 · answered Oct 27 '12 at 14:46

N = 1000;
x = [-20:20];
samples = 2 + 4*randn(N, 1);
ySamples = histc(samples,x) / N;
yTheoretical = pdf('norm', x, 2, 4);
plot(x, yTheoretical, x, ySamples)

randn(N, 1) creates an N-by-1 vector.

histc is histogram count by bins given in x - you can use hist to plot the result immediately, but here we want to divide it by N.

pdf contains many useful PDFs, normal is just one example.

score 0 · Answer 3 · answered Dec 13 '13 at 16:09

remember this: X ~ N(mean, variance)

randn in matlab produces normal distributed random variables W with zero mean and unit variance. To change the mean and variance to be the random variable X (with custom mean and variance), follow this equation: X = mean + standard_deviation*W Please be aware of that standard_deviation is square root of variance.

N = 1000;
x = [-20:20];
samples = 2 + sqrt(4)*randn(N, 1);
ySamples = histc(samples,x) / N;
yTheoretical = pdf('norm', x, 2, sqrt(4)); %put std_deviation not variance
plot(x, yTheoretical, x, ySamples)

score 0 · Answer 4 · edited Jul 08 '19 at 21:35

0

A quick and easy way to achieve this using one line of code is to use :

mu = 2;
sigma = 2;
samples = normrnd(mu,sigma,M,N);

This will generate an MxN matrix, sampled from N(μ,), (= N(2,2) in this particular case). For additional information, see normrnd.

edited Jul 08 '19 at 21:35

SecretAgentMan

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answered Jul 08 '19 at 12:17

user3009798

21
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How is this different from [this answer](https://stackoverflow.com/a/13101180/8239061) or [this one](https://stackoverflow.com/a/20570900/8239061)? Plus OP wanted N(2,4), not N(2,2). Also, question explicitly wants to look at the empirical [PDF](https://en.wikipedia.org/wiki/Probability_density_function) and compare to theoretical one. – SecretAgentMan Jul 08 '19 at 14:59

Creating Gaussian random variable with MATLAB

4 Answers4