MATLAB: How to generate numbers from probability mass function

do simulation with probability mass functiongenerate numbers from probability mass function

Hallo,

Given a probability mass function defined as P(X=3)=0.2, P(X=7)=0.3 and P(X=10)=0.5, I want to generate randomly 30 numbers (values for X) with this probability mass function as base. But I really have no idea how and where to start.

Can somebody help me?

Thank you in advance

Best Answer

n = 30;
X = zeros(n,1);
x = rand(n,1);
X(x <= 0.5) = 10;
X(x > 0.5 & x <= 0.8) = 7;
X(x > 0.8) = 3;

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MATLAB: Random samples from combination of poisson distributions

One easy way to generate a random score from a poisson mixture distribution is to randomly select the particular poisson first and then randomly select the number from that poisson, something like this:

% generate a random value of x from a poisson mixture distribution:
ru = rand;
if r1<0.2
    x = poissrnd(lambda1);  % prob = 0.2 that x comes from this distribution
elseif ru<0.5
    x = poissrnd(lambda2);  % prob = 0.3 that x comes from this distribution
else
    x = poissrnd(lambda3);  % prob = 0.5 that x comes from this distribution
end

There are various ways to vectorize this for lots of x's, but I'm not sure which would be fastest.

Did you just want the poisson mixture for generating random numbers, or did you want it for some other reason too?

MATLAB: Question about PDF(probability density function)

Those terms are often used interchangeably. However, there is a clear distinction between

Cumulative distribution function, or cumulative probability distribution function

and the probability density function.

The cumulative distribution function is the P(X \leq x), the probability that a random variable X assumes a value less than or equal to x. For continuous random variables, the probability density function is the derivative of the cumulative distribution function.

Sometimes people use probability distribution function for discrete random variables where you can actually talk about the probability for an elementary outcome (unlike continuous random variables where you have to talk about probability on an interval). The term probability density function is NOT used for discrete random variables. For discrete random variables, people often use the term probability mass function.

Myself when I use the term distribution function, I mean the cumulative distribution function (for both continuous and discrete RVs). So you have to decide from context how it is being used.

Best Answer

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MATLAB: Random samples from combination of poisson distributions

MATLAB: Question about PDF(probability density function)

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