#StackBounty: #confidence-interval #poisson-distribution #bernoulli-process confidence intervals for the Poisson process (lambda) samp…

Bounty: 50

Say, I have a Poisson process which was measured $N$ times, and each measurement produced $k_i$ value.
Also, $k_i$ are events that I have to detect and my detection probability is $p$. In fact, I detect $widetilde{k}_i$ which correlates with $k_i$ via $p$.

Knowing, the number of the detected events $widetilde{k}_i$, the constant probability $p$, and the constant measurement time $T$, how I find the confidence interval for estimation of Poisson’s $lambda$?


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