For those that may be interested, the solution to this problem is to use the Wilson interval. Details are available in the following paper. This interval can be calculated for any value of n and k, including for k = 0 (which was what I was interested in)...
Sorry, I meant to write \int_0^1 (1-p)^N dp = 1/(N+1), where N is fixed (total number of trials). The integrand looks just like an exp. decay exp(-Np), i.e., Poisson function, as you pointed out.
I can treat the integrand like a density function, and want to find the value of p = a, which...
OK, how about this... I'd be very grateful if someone could check this.
p is the true (population) probability. Given that, with binomial, prob. that I measure k = 0 from N trials is (1-p)^N.
We know 0\leq p\leq 1. So an experimental measurement of p_exp = 0 could have come from any value...
Thanks for your reply: I've been mulling over your suggestions.
One problem I have is that I don't know what the population p is, I estimate p = 0 from the results. I know my distribution is totally asymmetric: I know that p\geq0. The poisson approximation is asymmetric, so I see how that...
I have some data (4 runs each of about 10 trials) which is binomial with n_hits/N_trials
n/N = 0/11, 0/9, 0/10, 0/10
So, I estimate the probability p = n/N = 0
But how can I calculate an uncertainty on this value?
I thought to try
total N_tot=40 and n_tot=1, so p_tot=1/40 = 0.025
(i.e...