when does Poisson distribution approximate binomial distribution - what is n in an e-commerce setting I am quoting from here:
"As with many ideas in statistics, “large” and “small” are up to interpretation. A rule of thumb is the Poisson distribution is a decent approximation of the Binomial if n > 20 and np < 10. Therefore, a coin flip, even for 100 trials, should be modeled as a Binomial because np = 50. A call center which gets 1 call every 30 minutes over 120 minutes could be modeled as a Poisson distribution as np = 4."
Here n is trials with a probability p. I try to translate this into an e-commerce setting where we have websites which users can visit. I would think that np is the visiting rate. So in the above example there are 4 visitors within 120 minutes on average. I am sorry I do not get my head around what n is in my setting? I would think it has to do with conversions? Thanks.
 A: Binomial and Poisson distribution families are both distributions for counts, rather than continuous measures. The difference is in the cardinality: Poisson distributions are useful for unbound counts. Binomial distributions have an upper limit, which is the number of trials. Poisson distribution can be seen as a limiting case of infinite trials. The more trials a Binomial process has (at a very low success rate), the more it starts to look Poisson.
However, since Poisson and Binomial aka Logistic regression are equally well established and can both easily be estimated, it makes no sense to approximate one with the other. In essence, if you can precisely tell what the number of trials is, it is Binomial. If you can't tell it, it usually is Poisson.
Regarding your domain of e-commerce, examples of Poisson distributed variables would be number of visitors in a time frame or number of products in the cart. Binomial variables would be proportion of visits where sth is actually bought or number of test users that prefer design A over B.
