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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.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
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 .
The generalized normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however ...
These point estimates may be used as initial values that can be refined with more powerful methods, including a least-squares optimization, which has shown to work for the Multimodal Exponentially Modified Gaussian (MEMG) case. [8] A code implementation with analytical MEMG derivatives and an optional oscillation term for sound processing is ...
In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and precision matrix (the inverse of the covariance matrix ).
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Input points before kernel PCA. Consider three concentric clouds of points (shown); we wish to use kernel PCA to identify these groups. The color of the points does not represent information involved in the algorithm, but only shows how the transformation relocates the data points. First, consider the kernel