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matlabdistributionsampling
Mike Lang
Mike Lang

Reputation: 65

How to sample from delayed geometric distribution in matlab

What is the best and correct way to sample from a delayed geometric distribution (geometric distribution for positive integers greater 0) in matlab?

To my understanding the delayed geometric distribution is defined as follows, where f is the probability mass function:

f(k)= (1-p)*p^(k-1) for k=1,2,3... and 0<p<1

My current approach to sample from that distribution is to first solve for k and defining a function that returns a random value: 

function k = georndDel(p)
    f = rand;
    k = log(-(f*p)./(p-1))./log(p); %for log(p)<>0, 0<p<1
end

However, this returns a continuous value, sometimes negative, where I require only positive integers to be returned.

Is there amn obvious error in inverting the probability mass function? And how do I restrict the random values to positive ingegers?

Upvotes: 0

Views: 240

Answers (1)

Anton
Anton

Reputation: 4684

You can generate the numbers manually:

cdf_val = rand();

k = log(1-cdf_val)/log(1-p);
k = round(k+0.5);

Or as Luis already mentioned using the geornd() plus 1.

Here is an example:

p = 0.1;

n = 20000;

arr1=zeros(n, 1);
arr2=zeros(n, 1);

for i=1:n
    % manual approach
    cdf_val = rand();

    k = log(1-cdf_val)/log(1-p);
    arr1(i) = round(k+0.5);

    % using geornd
    arr2(i) = geornd(p)+1;
end

histogram(arr1, 0:60);
hold on;
histogram(arr2, 0:60);
hold off;
legend('manual', 'geornd+1')

generating delayed geometric distribution manually

Upvotes: 2

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