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  2. Pivotal quantity - Wikipedia

    en.wikipedia.org/wiki/Pivotal_quantity

    Then is called a pivotal quantity (or simply a pivot). Pivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels.

  3. Ancillary statistic - Wikipedia

    en.wikipedia.org/wiki/Ancillary_statistic

    A ancillary statistic is a specific case of a pivotal quantity that is computed only from the data and not from the parameters. They can be used to construct prediction intervals . They are also used in connection with Basu's theorem to prove independence between statistics.

  4. Fiducial inference - Wikipedia

    en.wikipedia.org/wiki/Fiducial_inference

    The calculation is identical to the pivotal method for finding a confidence interval, but the interpretation is different. In fact older books use the terms confidence interval and fiducial interval interchangeably. [citation needed] Notice that the fiducial distribution is uniquely defined when a single sufficient statistic exists.

  5. List of statistics articles - Wikipedia

    en.wikipedia.org/wiki/List_of_statistics_articles

    Encyclopedia of Statistical Sciences (book) Engineering statistics; Engineering tolerance; Engset calculation; Ensemble forecasting; Ensemble Kalman filter; Entropy (information theory) Entropy estimation; Entropy power inequality; Environmental statistics; Epi Info – software; Epidata – software; Epidemic model; Epidemiological methods ...

  6. t-statistic - Wikipedia

    en.wikipedia.org/wiki/T-statistic

    Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...

  7. Prediction interval - Wikipedia

    en.wikipedia.org/wiki/Prediction_interval

    For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is approximately 5 + (2⋅1) = 7, thus giving a prediction interval of ...

  8. Confidence interval - Wikipedia

    en.wikipedia.org/wiki/Confidence_interval

    A simple example arises where the quantity to be estimated is the population mean, in which case a natural estimate is the sample mean. Similarly, the sample variance can be used to estimate the population variance. A confidence interval for the true mean can be constructed centered on the sample mean with a width which is a multiple of the ...

  9. Student's t-distribution - Wikipedia

    en.wikipedia.org/wiki/Student's_t-distribution

    These problems are generally of two kinds: (1) those in which the sample size is so large that one may treat a data-based estimate of the variance as if it were certain, and (2) those that illustrate mathematical reasoning, in which the problem of estimating the standard deviation is temporarily ignored because that is not the point that the ...

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