I've been looking everywhere for a method of finding a given percentile from a Poisson distribution but can't seem to find much, so I figured I'd ask here if anyone knows.
How can I find a given percentile (say the 20th percentile) of a poisson distribution given the value of its parameter $\lambda$.
For example, if $X\sim \text{Pois}(4.5)$, how can I find the first 20th percentile of the distribution?
Best Answer
For a discrete distributions like the Poisson, it depends on how you define "percentiles".
Most statistics software programs will compute probabilities for the Poisson distribution. For example, using R, we can compute $P = P(X \le x)$ like this:
So you can see that the 20th percentile is between 2 and 3.