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Math Help - Combining 2 poisson processes?

  1. #1
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    Combining 2 poisson processes?

    Hi everyone
    can anyone help me understand how to merge two Poisson processes lets say λ1 and λ2 and how it can produce a new process with rate λ1+λ2.
    Thanks in advance.

    Regards
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  2. #2
    MHF Contributor
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    Re: Combining 2 poisson processes?

    Hey crystal11.

    By merge I assume you mean add them together where both are independent.

    The usual way to prove this is through moment generating functions but you can also use the convolution result: they are both aspects of the same idea, but they have different uses depending on what needs to be done analytically and statistically.

    Moment-generating function - Wikipedia, the free encyclopedia

    List of convolutions of probability distributions - Wikipedia, the free encyclopedia

    The proof from first principles is best done with the MGF to show that the products of two Poisson MGF's produce a Poisson MGF and since MGF unique represents a distribution, you're done.
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