The SAGE Encyclopedia of Educational Research, Measurement, and
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Zhiyong Zhang

doi:10.4135/9781506326139

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Moments of a Distribution

By: Zhiyong Zhang
In:The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation
Chapter DOI:https://doi.org/10.4135/9781506326139
Subject:Special & Inclusive Education (general), Emotional Intelligence
Keywords:distribution; kurtosis; skewness

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Moments of a Distribution

Moments are quantitative measures of a distribution function. Formally, the nth moment about a value c of a distribution f(x) is defined as

$\begin{array}{l} μ_{n} = E [(x - c)^{n}] = \\ {\begin{matrix} \sum {(x - c)}^{n} f (x) Discrete distibution \\ \int {(x - c)}^{n} f (x) d x Continuous distribution \end{matrix}} . \end{array}$

[Page 1084]When c = 0, they are called the raw moments, and when c is set at the mean of the distributions, ...

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  Zhang, Z. (2018). Moments of a distribution. In The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation (Vol. 4, pp. -). SAGE Publications, Inc., https://doi.org/10.4135/9781506326139
  
  Zhang, Zhiyong. "Moments of a Distribution." In The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation, . Thousand Oaks,: SAGE Publications, Inc., 2018. https://doi.org/10.4135/9781506326139.
  
  Zhang, Z. 2018. Moments of a Distribution. In: The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. Thousand Oaks,: SAGE Publications, Inc. pp. Available at: <https://doi.org/10.4135/9781506326139> [Accessed 5 Dec 2023].
  
  Zhang, Zhiyong. "Moments of a Distribution." The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. Vol. 4. Thousand Oaks,: SAGE Publications, Inc., 2018, pp. . Sage Knowledge, doi: https://doi.org/10.4135/9781506326139.
  
  Zhang, Zhiyong. Moments of a distribution. In The SAGE Encyclopedia of Educational Research, Measurement, and Evaluation. Vol. 4. Thousand Oaks,: SAGE Publications, Inc.; 2018: -. doi:10.4135/9781506326139
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