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A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product = is a product distribution.
The product of two Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the sum of the original variances: = +. The product of two Gaussian probability density functions (PDFs), though, is not in general a Gaussian PDF.
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 ...
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 ...
The squared Mahalanobis distance () is decomposed into a sum of k terms, each term being a product of three meaningful components. [6] Note that in the case when k = 1 {\displaystyle k=1} , the distribution reduces to a univariate normal distribution and the Mahalanobis distance reduces to the absolute value of the standard score .
Gaussian Uncorrelated Manually Manually No No Manually STK; GSTools: GNU LGPL: Python: Yes No No ND No Gaussian Yes Yes Yes Yes No No GSTools; PyKrige: BSD: Python: Yes No No 2D,3D No Gaussian i.i.d. No No No No No PyKrige; GPR: Apache: C++: Yes No Sparse ND No Gaussian i.i.d. Some, Manually Manually First No No GPR; celerite2: MIT: Python: No ...
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision .