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The log-normal distribution is the maximum entropy probability distribution ... For example, the log-normal ... has a normal (i.e., Gaussian) distribution ...
The log-Laplace distribution; The log-logistic distribution; The log-metalog distribution, which is highly shape-flexile, has simple closed forms, can be parameterized with data using linear least squares, and subsumes the log-logistic distribution as a special case. The log-normal distribution, describing variables which can be modelled as the ...
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 ...
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then
For example, some authors [6] ... suppose X follows a Gaussian distribution i.e. ... The logarithm of a characteristic function is a cumulant generating function, ...
This case arises frequently in statistics; for example, in the distribution of the vector of residuals in the ordinary least squares regression. The X i {\displaystyle X_{i}} are in general not independent; they can be seen as the result of applying the matrix A {\displaystyle {\boldsymbol {A}}} to a collection of independent Gaussian variables ...
Example rotations of Gaussian blobs can be seen in the following examples: ... Gaussian distribution: ... the Gaussian parameters is to take the logarithm of the data ...
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function ... such as the log-normal distribution, for example. ...