Date: Fri, 8 Dec 2023 05:18:28 +0000 (UTC) Message-ID: <807652265.2394.1702012708969@localhost> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_2393_235053810.1702012708968" ------=_Part_2393_235053810.1702012708968 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Introduction - Binomial Process

# Estimating a binomial probability or a pro= portion p using classical statistics

In many problems, we need to determin= e 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 w= ill have had some trials n, of which s were successes. This section describ= es three methods:

Binomial distribution method

The crudest method, not recommended, but explained so you know why to av= oid it.

Commonly used. It offers some improvement over the binomial method, but = still cannot be applied when s =3D 0 or n, and gives inco= rrect results at extremes.

Mid-p cumulative confidence constru= ction

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 i= f the Binomial outcome is present.

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