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Binomial distribution/confidence question for dummies
(The 'dummy' would be me.)
I have an event that happens with unknown probability p. Each of n independent events results in k of these events happening. How do I construct a (95%) confidence interval for p?
For small n it's easy to figure this out with numerical combinatorics:
Pr(at most k events) = [tex]\sum_{i=0}^k{n\choose i}p^i(1-p)^{n-i}[/tex]
Pr(at least k events) = [tex]\sum_{i=k}^n{n\choose i}p^i(1-p)^{n-i}[/tex]
and then find the roots of Pr(at most k events) - 0.05 and Pr(at least k events) - 0.05. (Maybe I should use 0.025 instead?)
But for large n (even not all that large!), this is inconvenient. Surely there is some standard statistical method for this? Sticking as close to the roots as possible would be best -- I'd prefer to use as little Central Limit Theorem as I can.
(The 'dummy' would be me.)
I have an event that happens with unknown probability p. Each of n independent events results in k of these events happening. How do I construct a (95%) confidence interval for p?
For small n it's easy to figure this out with numerical combinatorics:
Pr(at most k events) = [tex]\sum_{i=0}^k{n\choose i}p^i(1-p)^{n-i}[/tex]
Pr(at least k events) = [tex]\sum_{i=k}^n{n\choose i}p^i(1-p)^{n-i}[/tex]
and then find the roots of Pr(at most k events) - 0.05 and Pr(at least k events) - 0.05. (Maybe I should use 0.025 instead?)
But for large n (even not all that large!), this is inconvenient. Surely there is some standard statistical method for this? Sticking as close to the roots as possible would be best -- I'd prefer to use as little Central Limit Theorem as I can.
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