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Thread: Proof CDF for Poisson distribution

  1. #1
    Junior Member
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    Proof CDF for Poisson distribution

    Hello,
    How can proof and write CDF for Poisson distribution?
    (Later: I need CDF for Poisson distribution to generate random number.)
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  2. #2
    Senior Member zzephod's Avatar
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    Re: Proof CDF for Poisson distribution

    The usual (not always the best for large $\lambda$) way of generating Poisson distributes psuedo random numbers is to use Knuth's algorithm.

    Psuedo-code for this is shwn below:

    Code:
    function PRN(lambda)
    % -------------------------------------------------------------
    % Generate a random value from the (discrete) Poisson 
    % distribution with parameter lambda, using Knuth's Algorithm.
    %
    % See pages 132-3 of v2 TAOCP, Semi-Numerical Algorithms 2nd Ed. Don Knuth 1981.
    %
    %--------------------------------------------------------------
      k=0;prod=UniformRand;
      repeat
        if prod<=exp(-lambda)  
             break
        endif
        prod=prod*UniformRand;
        k=k+1;
      end
      return k
    endfunction
    Last edited by zzephod; Dec 7th 2016 at 01:44 AM.
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  3. #3
    MHF Contributor
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    Re: Proof CDF for Poisson distribution

    Hey life24.

    The proof for a Poisson distribution is based on taking a Binomial distribution and finding out what happens when you have an infinite number of trials before converting it to a rate process [instead of a counting process].

    https://en.wikipedia.org/wiki/Poisson_distribution

    Try taking a binomial distribution, send the count to infinity and normalize it so that you get a rate instead of a count.
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