What kind of confidence interval does
scipy.stats.poisson.interval return? Is it normal approximation? I went on GitHub, but could not look it up in the code. How can I look it up in the code?
It's not a confidence interval. The
scipy.stats.poisson object is a subclass of the
scipy.stats.rv_discrete class (i.e., its "parent" class). The parent class defines the
.interval method here: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.interval.html#scipy.stats.rv_discrete.interval
Specifically, this method returns an interval that gives equal probability on either side of the median. Unfortunately, they do erroneously call this a confidence interval, even though its just a plain old interval of a probability distribution. For example, a 90% interval would give the values that are at the 5th and 95th percentiles, since both of these are 45% above or below the median.
You'll notice that both this description on the one for the poisson both say that it is an interval that captures a
alpha percent of the distribution. Hence, this is really not a confidence interval, but a probability interval (it contains
alpha percent of the total probability).