Definition: Confidence interval
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Estimation theory ▷ Interval estimates ▷ Confidence interval
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Metadata: ID: D174 | shortcut: ci | author: JoramSoch | date: 2022-03-27, 23:56.
Definition: Let $y$ be a random sample from a probability distributions governed by a parameter of interest $\theta$ and quantities not of interest $\varphi$. A confidence interval for $\theta$ is defined as an interval $[u(y), v(y)]$ determined by the random variables $u(y)$ and $v(y)$ with the property
\[\label{eq:ci} \mathrm{Pr}(u(y) < \theta < v(y) \, \vert \, \theta, \varphi) = \gamma \quad \text{for all} \quad (\theta, \varphi) \; .\]where $\gamma = 1 - \alpha$ is called the confidence level.
- Wikipedia (2022): "Confidence interval"; in: Wikipedia, the free encyclopedia, retrieved on 2022-03-27; URL: https://en.wikipedia.org/wiki/Confidence_interval#Definition.
Metadata: ID: D174 | shortcut: ci | author: JoramSoch | date: 2022-03-27, 23:56.