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This probability distribution highlights some different confidence intervals. In frequentist statistics, a confidence interval (CI) is an interval which is expected to contain the parameter being estimated. More specifically, a CI is a random interval which contains the parameter being estimated at a given percentage of the time (under ...
In Bayesian statistics, a credible interval is an interval used to characterize a probability distribution. It is defined such that an unobserved parameter value has a particular probability γ {\displaystyle \gamma } to fall within it.
By contrast, the (true) coverage probability is the actual probability that the interval contains the parameter. If all assumptions used in deriving a confidence interval are met, the nominal coverage probability will equal the coverage probability (termed "true" or "actual" coverage probability for emphasis).
A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality ...
An absolutely continuous probability distribution is a probability distribution on the real numbers with uncountably many possible values, such as a whole interval in the real line, and where the probability of any event can be expressed as an integral. [19]
In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. [1] The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method). [2]
If each interval individually has coverage probability 0.95, the simultaneous coverage probability is generally less than 0.95. A 95% simultaneous confidence band is a collection of confidence intervals for all values x in the domain of f(x) that is constructed to have simultaneous coverage probability 0.95.