Probability distributions

Kaniadakis Gaussian distribution

The Kaniadakis Gaussian distribution (also known as κ-Gaussian distribution) is a probability distribution which arises as a generalization of the Gaussian distribution from the maximization of the Kaniadakis entropy under appropriated constraints. It is one example of a Kaniadakis κ-distribution. The κ-Gaussian distribution has been applied successfully for describing several complex systems in economy, geophysics, astrophysics, among many others. The κ-Gaussian distribution is a particular case of the κ-Generalized Gamma distribution. (Wikipedia).

Kaniadakis Gaussian distribution
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Multivariate Gaussian distributions

Properties of the multivariate Gaussian probability distribution

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(PP 6.8) Marginal distributions of a Gaussian

For any subset of the coordinates of a multivariate Gaussian, the marginal distribution is multivariate Gaussian.

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(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian

An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.

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(ML 7.9) Posterior distribution for univariate Gaussian (part 1)

Computing the posterior distribution for the mean of the univariate Gaussian, with a Gaussian prior (assuming known prior mean, and known variances). The posterior is Gaussian, showing that the Gaussian is a conjugate prior for the mean of a Gaussian.

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(ML 7.10) Posterior distribution for univariate Gaussian (part 2)

Computing the posterior distribution for the mean of the univariate Gaussian, with a Gaussian prior (assuming known prior mean, and known variances). The posterior is Gaussian, showing that the Gaussian is a conjugate prior for the mean of a Gaussian.

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Related pages

Error function | Friedmann–Lemaître–Robertson–Walker metric | Kaniadakis Gamma distribution | Kaniadakis Weibull distribution | Normal distribution | Random variable | Kaniadakis Erlang distribution | Shape parameter | Kurtosis | Kaniadakis distribution | Extreme value theory | Real number | Probability distribution | Cumulative distribution function | Inverse problem | Financial models with long-tailed distributions and volatility clustering