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  2. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    For example, the exponential function is the function which is equal to its own derivative everywhere, and assumes the value 1 at the origin. However, one may equally well define an analytic function by its Taylor series. Taylor series are used to define functions and "operators" in diverse areas of mathematics. In particular, this is true in ...

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

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

    In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite.

  4. Taylor's law - Wikipedia

    en.wikipedia.org/wiki/Taylor's_law

    where s 2 is the variance and m is the mean. If the population obeys Taylor's law = The ICS is also equal to Katz's test statistic divided by ( n / 2 ) 1/2 where n is the sample size. It is also related to Clapham's test statistic. It is also sometimes referred to as the clumping index.

  5. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1715, [2] although an earlier version of the result was already mentioned in 1671 by James Gregory. [ 3 ] Taylor's theorem is taught in introductory-level calculus courses and is one of the central elementary tools in mathematical analysis .

  6. Experimental uncertainty analysis - Wikipedia

    en.wikipedia.org/wiki/Experimental_uncertainty...

    4. The solution is to expand the function z in a second-order Taylor series; the expansion is done around the mean values of the several variables x. (Usually the expansion is done to first order; the second-order terms are needed to find the bias in the mean. Those second-order terms are usually dropped when finding the variance; see below). 5.

  7. First-order second-moment method - Wikipedia

    en.wikipedia.org/wiki/First-order_second-moment...

    For the second-order approximations of the third central moment as well as for the derivation of all higher-order approximations see Appendix D of Ref. [3] Taking into account the quadratic terms of the Taylor series and the third moments of the input variables is referred to as second-order third-moment method. [4]

  8. Propagation of uncertainty - Wikipedia

    en.wikipedia.org/wiki/Propagation_of_uncertainty

    The Taylor expansion would be: + where / denotes the partial derivative of f k with respect to the i-th variable, evaluated at the mean value of all components of vector x. Or in matrix notation , f ≈ f 0 + J x {\displaystyle \mathrm {f} \approx \mathrm {f} ^{0}+\mathrm {J} \mathrm {x} \,} where J is the Jacobian matrix .

  9. Ratio estimator - Wikipedia

    en.wikipedia.org/wiki/Ratio_estimator

    Another estimator based on the Taylor expansion is [3] = where n is the sample size, N is the population size, m x is the mean of the x variate and s x 2 and s y 2 are the sample variances of the x and y variates respectively.