If the rate of a Poisson process follows Gamma distribution, it is known that the total number of arrivals follows a negative binomial distribution. How about the conditional distribution of the increments of the Poisson process, i.e., $\mathbb{P}(N(t+h)=m|N(t)=n)$
2026-03-26 22:15:15.1774563315
Distribution of the increments of a Poisson Process with random rate
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