Question

Using MATLAB, you have to start with a uniform distribution between (0,1). You need to generate the following sequences of random variables:

1.Rayleigh distributed random variable. (a=0, b=1).

2.Exponentially R.V. (a=0, b=1)

3.Gaussian R.V. (a=0, (σX)=2)

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At least, give me a MATLAB code of the first one.

I tired many time to solve it using this equation:

but it didn’t work with me.

Answer 1

Here are the formulas, it’s easy to implement them in Matlab:

1. Generating Rayleigh-distributed random variates
2. Generating exponential variates
3. Generating values from Gaussian distribution

The first two methods are based on Inverse Transform Sampling. In the third case, the CDF cannot be inverted analytically, so ITS doesn’t work, and special techniques are needed.

EDIT

Example (Rayleigh):

n = 10000; % number of variates
u = rand(n, 1); % generating uniform variates
sigma = 1; % the parameter
x = sigma * sqrt(-2 * log(u)); % generating Rayleigh-distributed variates
hist(x, 50); % histogram