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  2. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    All these extensions are also called normal or Gaussian laws, so a certain ambiguity in names exists. The multivariate normal distribution describes the Gaussian law in the k-dimensional Euclidean space. A vector X ∈ R k is multivariate-normally distributed if any linear combination of its components Σ k j=1 a j X j has a (univariate) normal ...

  3. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.

  4. List of integrals of Gaussian functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Owen [1] has an extensive list of Gaussian-type integrals; only a subset is given below. Indefinite integrals ... Handbook of the normal distribution (2nd ed.). CRC ...

  5. Matrix normal distribution - Wikipedia

    en.wikipedia.org/wiki/Matrix_normal_distribution

    The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ⁡ ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...

  6. Multivariate normal distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_normal...

    The fact that two random variables and both have a normal distribution does not imply that the pair (,) has a joint normal distribution. A simple example is one in which X has a normal distribution with expected value 0 and variance 1, and = if | | > and = if | | <, where >. There are similar counterexamples for more than two random variables.

  7. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Specifically, if the mass-density at time t=0 is given by a Dirac delta, which essentially means that the mass is initially concentrated in a single point, then the mass-distribution at time t will be given by a Gaussian function, with the parameter a being linearly related to 1/ √ t and c being linearly related to √ t; this time-varying ...

  8. Generalized normal distribution - Wikipedia

    en.wikipedia.org/.../Generalized_normal_distribution

    So there is no strong reason to prefer the "generalized" normal distribution of type 1, e.g. over a combination of Student-t and a normalized extended Irwin–Hall – this would include e.g. the triangular distribution (which cannot be modeled by the generalized Gaussian type 1). A symmetric distribution which can model both tail (long and ...

  9. Orders of magnitude (probability) - Wikipedia

    en.wikipedia.org/wiki/Orders_of_magnitude...

    Gaussian distribution: probability of a value being more than 2 standard deviations from the mean on a specific side [17] 2.7×10 −2: Probability of winning any prize in the Powerball with one ticket in 2006 3.3×10 −2: Probability of a human giving birth to twins [19] 4.8×10 −2: Probability of being dealt a two pair in poker 10 −1 ...

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