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  2. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Pearson_correlation...

    Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.

  3. Taylor expansions for the moments of functions of random ...

    en.wikipedia.org/wiki/Taylor_expansions_for_the...

    The above is obtained using a second order approximation, following the method used in estimating the first moment. It will be a poor approximation in cases where () is highly non-linear. This is a special case of the delta method.

  4. Point-biserial correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Point-biserial_correlation...

    The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable X and a dichotomous variable Y, r XY = r pb. This can be shown by assigning two distinct numerical values to the dichotomous variable.

  5. Method of simulated moments - Wikipedia

    en.wikipedia.org/wiki/Method_of_simulated_moments

    In econometrics, the method of simulated moments (MSM) (also called simulated method of moments [1]) is a structural estimation technique introduced by Daniel McFadden. [2] It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integrals.

  6. Factorial moment - Wikipedia

    en.wikipedia.org/wiki/Factorial_moment

    In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable.Factorial moments are useful for studying non-negative integer-valued random variables, [1] and arise in the use of probability-generating functions to derive the moments of discrete random variables.

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  8. Rank correlation - Wikipedia

    en.wikipedia.org/wiki/Rank_correlation

    The only pair that does not support the hypothesis are the two runners with ranks 5 and 6, because in this pair, the runner from Group B had the faster time. By the Kerby simple difference formula, 95% of the data support the hypothesis (19 of 20 pairs), and 5% do not support (1 of 20 pairs), so the rank correlation is r = .95 − .05 = .90.

  9. Moment matrix - Wikipedia

    en.wikipedia.org/wiki/Moment_matrix

    In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices .)

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