I want to know which event has the best score (or luck or odd)
$p$ (prob of success) is equal with all event. There are givne set of events, that is (number of try, number of success)
$$\mathrm{event1} (n_1, x_2) \sim \mathcal{B}(n_1,P)$$ $$\mathrm{event2} (n_2, x_2) \sim \mathcal{B}(n_2,P)$$ $$\dots$$ $$\mathrm{event99} (n_{99}, x_{99}) \sim \mathcal{B}(n_{99},P)$$
The number of trials,success is all different.
And how compare probability of each cases? for example, ranking NO.1 = event33 / ranking NO.2 = event44 / ... ranking NO.99 = event11
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In the same trial, the more success In the same success, the less trial
Q1. I try cdf of Binomial distribution. (quantile) But I don't know it is okay. Because Binomial distribution has diffrent distribution with different number of trial.
Q2. so, I try2 Normal distribution approximation. But N is not big enough.
Q3. and I don't know if I should use the negative binomial distribution. In that cases, the prob of binomial dist is bed.. there are too many 1
Thank you