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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. Intelligence and personality - Wikipedia

    en.wikipedia.org/wiki/Intelligence_and_personality

    Intelligence and personality have traditionally been studied as separate entities in psychology, but more recent work has increasingly challenged this view. An increasing number of studies have recently explored the relationship between intelligence and personality , in particular the Big Five personality traits .

  4. Information geometry - Wikipedia

    en.wikipedia.org/wiki/Information_geometry

    Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. [ 1 ] It studies statistical manifolds , which are Riemannian manifolds whose points correspond to probability distributions .

  5. 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.

  6. 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 ...

  7. Symmetric function - Wikipedia

    en.wikipedia.org/wiki/Symmetric_function

    In statistics, an -sample statistic (a function in variables) that is obtained by bootstrapping symmetrization of a -sample statistic, yielding a symmetric function in variables, is called a U-statistic. Examples include the sample mean and sample variance.

  8. Bayesian probability - Wikipedia

    en.wikipedia.org/wiki/Bayesian_probability

    Bayesian probability (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation [2] representing a state of knowledge [3] or as quantification of a personal belief.

  9. 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.

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