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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. Correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Correlation_coefficient

    The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations. [4]

  5. Distribution of the product of two random variables - Wikipedia

    en.wikipedia.org/wiki/Distribution_of_the...

    The distribution of the product of correlated non-central normal samples was derived by Cui et al. [11] and takes the form of an infinite series of modified Bessel functions of the first kind. Moments of product of correlated central normal samples. For a central normal distribution N(0,1) the moments are

  6. 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 .)

  7. 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.

  8. 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.

  9. Factorial moment generating function - Wikipedia

    en.wikipedia.org/wiki/Factorial_moment...

    In probability theory and statistics, the factorial moment generating function (FMGF) of the probability distribution of a real-valued random variable X is defined as = ⁡ [] for all complex numbers t for which this expected value exists.

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