List of convolutions of probability distributions information
In probability theory, 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. Many well known distributions have simple convolutions. The following is a list of these convolutions. Each statement is of the form
where are independent random variables, and is the distribution that results from the convolution of . In place of and the names of the corresponding distributions and their parameters have been indicated.
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well known distributions have simple convolutions. The following is a listof these convolutions. Each statement is of the form ∑ i = 1 n X i ∼ Y {\displaystyle...
Many probabilitydistributions that are important in theory or applications have been given specific names. The Bernoulli distribution, which takes value...
In probability theory and statistics, there are several relationships among probabilitydistributions. These relations can be categorized in the following...
the listofconvolutionsofprobabilitydistributions, where the distributions to be convolved are those of the logarithms of the components of the product...
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probabilitydistribution for a real-valued...
exponential families ofdistributions. This is a large class ofprobabilitydistributions that includes the exponential distribution as one of its members, but...
algorithm Not to be confused with: listofconvolutionsofprobabilitydistributions Product distribution Mixture (probability) Mixture model Graphical model...
in probability theory ListofprobabilitydistributionsListofconvolutionsofprobabilitydistributions Glossary of experimental design Glossary of probability...
or more layers that perform convolutions. Typically this includes a layer that performs a dot product of the convolution kernel with the layer's input...
variables Listofconvolutionsofprobabilitydistributions – the probability measure of the sum of independent random variables is the convolutionof their...
Woldemar Voigt) is a probabilitydistribution given by a convolutionof a Cauchy-Lorentz distribution and a Gaussian distribution. It is often used in...
p)g(x,p).} 1. W(x, p) is a real-valued function. 2. The x and p probabilitydistributions are given by the marginals: ∫ − ∞ ∞ d p W ( x , p ) = ⟨ x | ρ...
partially continuous distribution, using a probability density function (which is normally used to represent absolutely continuous distributions). For example...
output probabilities, and increasing the value of b will create probabilitydistributions that are more concentrated around the positions of the largest...
and has some of the qualitative features of the normal density. The convolutions were computed via the discrete Fourier transform. A listof values y =...
1]} , and the strategy set for the generator contains arbitrary probabilitydistributions μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . However...
functions" to tempered distributions. The set of tempered distributions forms a vector subspace of the space ofdistributions D ′ ( U ) {\displaystyle...
quantities that provide an alternative to the moments of the distribution. Any two probabilitydistributions whose moments are identical will have identical...
for classification, one can add a shallow MLP on top of it that outputs a probabilitydistribution over classes. The original paper uses a linear-GeLU-linear-softmax...
classifier that is able to predict, given an observation of an input, a probabilitydistribution over a set of classes, rather than only outputting the most likely...
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