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  2. Symmetric derivative - Wikipedia

    en.wikipedia.org/wiki/Symmetric_derivative

    The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist. [1] [2]: 6 Neither Rolle's theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved.

  3. Supersymmetric theory of stochastic dynamics - Wikipedia

    en.wikipedia.org/wiki/Supersymmetric_Theory_of...

    Supersymmetric theory of stochastic dynamics (STS) is a multidisciplinary approach to stochastic dynamics on the intersection of dynamical systems theory, statistical physics, stochastic differential equations (SDE), topological field theories, and the theory of pseudo-Hermitian operators. The theory can be viewed as a generalization of the ...

  4. Symmetry of second derivatives - Wikipedia

    en.wikipedia.org/wiki/Symmetry_of_second_derivatives

    The derivative of an integrable function can always be defined as a distribution, and symmetry of mixed partial derivatives always holds as an equality of distributions. The use of formal integration by parts to define differentiation of distributions puts the symmetry question back onto the test functions , which are smooth and certainly ...

  5. Time reversibility - Wikipedia

    en.wikipedia.org/wiki/Time_reversibility

    A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed.. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time.

  6. Student's t-distribution - Wikipedia

    en.wikipedia.org/wiki/Student's_t-distribution

    In probability theory and statistics, Student's t distribution (or simply the t distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped.

  7. Statistical theory - Wikipedia

    en.wikipedia.org/wiki/Statistical_theory

    The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.

  8. Stochastic gradient descent - Wikipedia

    en.wikipedia.org/wiki/Stochastic_gradient_descent

    However, in statistics, it has been long recognized that requiring even local minimization is too restrictive for some problems of maximum-likelihood estimation. [3] Therefore, contemporary statistical theorists often consider stationary points of the likelihood function (or zeros of its derivative, the score function , and other estimating ...

  9. Symmetric probability distribution - Wikipedia

    en.wikipedia.org/wiki/Symmetric_probability...

    In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some ...

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