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  2. Central moment - Wikipedia

    en.wikipedia.org/wiki/Central_moment

    The first central moment μ 1 is 0 (not to be confused with the first raw moment or the expected value μ). The second central moment μ 2 is called the variance, and is usually denoted σ 2, where σ represents the standard deviation. The third and fourth central moments are used to define the standardized moments which are used to define ...

  3. Standardized moment - Wikipedia

    en.wikipedia.org/wiki/Standardized_moment

    In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree central moment) that is normalized, typically by a power of the standard deviation, rendering the moment scale invariant. The shape of different probability distributions can be compared using standardized moments. [1]

  4. Moment (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Moment_(mathematics)

    In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.

  5. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density , mean and variance , the moment generating function exists and is equal to

  6. Image moment - Wikipedia

    en.wikipedia.org/wiki/Image_moment

    Zhang et al. applied Hu moment invariants to solve the Pathological Brain Detection (PBD) problem. [6] Doerr and Florence used information of the object orientation related to the second order central moments to effectively extract translation- and rotation-invariant object cross-sections from micro-X-ray tomography image data. [7]

  7. Talk:Moment (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Talk:Moment_(mathematics)

    The kurtosis κ is defined to be the normalized fourth central moment minus 3. The kurtosis κ is defined to be the normalized fourth central moment - 3. In the second of these expressions, the hyphen used as a minus sign could be mistaken for a dash, so it's like saying: The kurtosis κ is defined to be the US president - George W. Bush.

  8. Skewness - Wikipedia

    en.wikipedia.org/wiki/Skewness

    where μ is the mean, σ is the standard deviation, E is the expectation operator, μ 3 is the third central moment, and κ t are the t-th cumulants. It is sometimes referred to as Pearson's moment coefficient of skewness , [ 5 ] or simply the moment coefficient of skewness , [ 4 ] but should not be confused with Pearson's other skewness ...

  9. Cumulant - Wikipedia

    en.wikipedia.org/wiki/Cumulant

    That is, when the addends are statistically independent, the mean of the sum is the sum of the means, the variance of the sum is the sum of the variances, the third cumulant (which happens to be the third central moment) of the sum is the sum of the third cumulants, and so on for each order of cumulant.