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  2. Inverse Gaussian distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse_Gaussian_distribution

    The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an "inverse" only in that, while the Gaussian describes a Brownian motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian motion with positive drift takes to reach a ...

  3. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

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  4. Inverse distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse_distribution

    Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters. In the algebra of random variables , inverse distributions are special cases of the class of ratio distributions , in which the numerator random variable has a degenerate distribution .

  5. List of probability distributions - Wikipedia

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

    The normal distribution, also called the Gaussian or the bell curve. It is ubiquitous in nature and statistics due to the central limit theorem: every variable that can be modelled as a sum of many small independent, identically distributed variables with finite mean and variance is approximately normal. The normal-exponential-gamma distribution

  6. Characteristic function (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_function...

    For example, some authors [6] define φ X (t) = E[e −2πitX], which is essentially a change of parameter. Other notation may be encountered in the literature: p ^ {\displaystyle \scriptstyle {\hat {p}}} as the characteristic function for a probability measure p , or f ^ {\displaystyle \scriptstyle {\hat {f}}} as the characteristic function ...

  7. Inverse-gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse-gamma_distribution

    In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.

  8. Normal-inverse-gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Normal-inverse-gamma...

    In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance .

  9. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.