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  1. Significance of the moments

    The n-th raw moment (i.e., moment about zero) of a random variable with density function is defined by The n-th moment of a
    It … See more

    Cumulants

    The first raw moment and the second and third unnormalized central moments are additive in the sense that if X and Y are independent random variables then
    (These can also hold for variables that satisfy wea… See more

    Sample moments

    For all k, the k-th raw moment of a population can be estimated using the k-th raw sample moment applied to a sample X1, ..., Xn drawn from the population.
    It can be shown that the expected value of the raw sa… See more

    Partial moments

    Partial moments are sometimes referred to as "one-sided moments." The n-th order lower and upper partial moments with respect to a reference point r may be expressed as
    If the integr… See more

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