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We know that merging two Poisson processes results in another Poisson process with a rate that is the sum of the two original rates. (https://www.probabilitycourse.com/chapter11/11_1_3_merging_and_splitting_poisson_processes.php)

What type of process do we get by merging two processes with lognormal (interarrival time) distributions? How are the parameters of this process related to the parameters of the original lognormal processes?

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  • $\begingroup$ does "merging" have to mean sum? $\endgroup$
    – Taylor
    Commented Jan 21, 2017 at 19:50
  • $\begingroup$ Merging means "combing" the event times. $\endgroup$
    – Tamas Kalmar-Nagy
    Commented Jan 21, 2017 at 20:23

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