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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- Nov 15th 2012, 06:27 AMcrystal11Combining 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 - Nov 15th 2012, 04:38 PMchiroRe: 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.