Random Numbers with Gaussian and Uniform Distributions in matlab

Question

I want generate a number in Gaussian and Uniform distributions in matlab. I know this function randi and rand() but all of them are in normal (Gau

Answer 1

It is true you can generate just about anything from rand but that it isn't always convenient, especially for some complicated distributions.

MATLAB has introduced Probability Distribution Objects which make this a lot easier and allow you to seamless access mean, var, truncate, pdf, cdf, icdf (inverse transform), median, and other functions.

You can fit a distribution to data. In this case, we use makedist to define the probability distribution object. Then we can generate using random.

% Parameters
mu = 10; 
sigma = 3;
a = 5; b = 15;
N = 5000;

% Older Approaches Still Work
rng(1775)
Z = randn(N,1);    % Standard Normal  Z~N(0,1)
X = mu + Z*sigma;  % X ~ Normal(mu,sigma)

U = rand(N,1);     % U ~ Uniform(0,1)
V = a + (b-a)*U;   % V ~ Uniform(a,b)

% New Approaches Are Convenient
rng(1775)
pdX = makedist('Normal',mu,sigma);
X2 = random(pdX,N,1);

pdV = makedist('Uniform',a,b);
V2 = random(pdV,N,1);

A reproducible example:

Support = (0:0.01:20)';
figure 
s(1) = subplot(2,2,1)
h(1) = histogram(X,'Normalization','pdf')
xlabel('Normal')
s(2) = subplot(2,2,2)
h(2) = histogram(V,'Normalization','pdf')
xlabel('Uniform')
s(3) = subplot(2,2,3), hold on, box on
h(3) = histogram(X2,'Normalization','pdf')
plot(Support,pdf(pdX,Support),'r-','LineWidth',1.2)
xlabel('Normal (new)')
s(4) = subplot(2,2,4), hold on, box on
h(4) = histogram(V2,'Normalization','pdf')
plot(Support,pdf(pdV,Support),'r-','LineWidth',1.2)
xlabel('Uniform (new)')
xlim(s,[0 20])  

References:
Uniform Distribution
Normal (Gaussian) Distribution