Estimating a binomial probability or a proportion p using classical statistics
In many problems, we need to determine a binomial probability (e.g. probability of a flood in a certain week of the year), or a proportion (e.g. the proportion of components that are made to a certain tolerance). To estimate the probability or proportion p you will have had some trials n, of which s were successes. This section describes three methods:
The crudest method, not recommended, but explained so you know why to avoid it.
Commonly used. It offers some improvement over the binomial method, but still cannot be applied when s = 0 or n, and gives incorrect results at extremes.
The best method that works for all values of s and n. It is also closely aligned to Bayesian results. Useful when we don't know if the Binomial outcome is present.