CODEWITHSUNDEEP
matlab
Shorty
Shorty

Reputation: 21

Generating random numbers from a piecewise probability distrubution in matlab

I am trying to input the following piecewise function into matlab as a probability distribution. Then I'm trying to generate random values of X. I have the statistic tool box so I can generate the random numbers using that, but I cannot figure out how to input the function so that I can actually generate the random numbers.

P(X)= Ax 0<=x<1
      A/2 1<=x<2
      0 otherwise

A is a normalization constant.

I ultimately want to show a histogram of 10,000 trials from this distribution and find the mean and standard deviation of my simulation.

Upvotes: 2

Views: 2573

Answers (1)

Jirka cigler
Jirka cigler

Reputation: 405

samples from given distribution can be generated for instance using inverse transform sampling (see http://en.wikipedia.org/wiki/Inverse_transform_sampling) It's quite easy since you just generate uniformly distributed values and then compute inverse of your cumulative distribuition function

Cumulative distrib. function can be computed by integration of propability density function, in your case

x^2/2 ... x from <0,1>

x/2 ... x from (1,2>

Note, that the normalizing constant is A=1 now, the m-file doing this is the following

function vals =genDist(len)
vals =  rand(len,1);
for i=1:length(vals)
    if vals(i)<=1/2 % vals(i) 0..0.5
        vals(i) = sqrt(2*vals(i));%inverse function of x^2/2 
    else % vals(i) 0.5-1
        vals(i) = vals(i)*2; %inverse function of x/2
    end
end

end

Upvotes: 2

Related Questions