Search code examples
matlabprobabilitygaussianprobability-density

Plot PDF of log-normal distribution

I'm using the randn function to generate a Gaussian random variable x1 with mean 0 and variance 1. After generating x1, I generate another Gaussian random variable x with mean m and variance σ2, that is: x = m + sqrt(σ)·x1.

I want to create a log-normal random variable y = ex and plot its PDF. I think I can use the histogram function to do this:

N = 10^5;          %// sample
x1 = randn(N,1);
m = 0;             %// mean of x1
sigma = 1;         %// variance of x1
x = m + sigma.*x1; %// create x
y = exp(x); 
figure;
hist(y);

and here is the diagram I get:

diagram

I think that my result is wrong but I don't know how to fix it.

Thank you so much! :)

Solution

  • The lognormal distribution can have a very long tail (i.e., even for large y the prob(y) > 0 and not vanishing.
    If you want to compare your pdf plot to those of e.g., the wiki web page, you will need to ignore the tail.

    bins = linspace(0,5,500);
n = hist( y, bins );
bar( bins(1:end-1), n(1:end-1)/N ); axis([0 bins(end-1) 0 1]); % discard last bin that has the "tail"