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In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to ...
In probability theory and statistics, the asymmetric Laplace distribution (ALD) is a continuous probability distribution which is a generalization of the Laplace distribution. Just as the Laplace distribution consists of two exponential distributions of equal scale back-to-back about x = m, the asymmetric Laplace consists of two exponential ...
The Landau distribution; The Laplace distribution; The Lévy skew alpha-stable distribution or stable distribution is a family of distributions often used to characterize financial data and critical behavior; the Cauchy distribution, Holtsmark distribution, Landau distribution, Lévy distribution and normal distribution are special cases.
In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters μ and b, then Y = e X has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.
The asymmetric multivariate Laplace distribution is not elliptical unless =, in which case the distribution reduces to the symmetric multivariate Laplace distribution with =. [ 1 ] The probability density function (pdf) for a k -dimensional asymmetric multivariate Laplace distribution is:
Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) / and the uniform probability /. Invoking Laplace's rule of succession , some authors have argued [ citation needed ] that α should be 1 (in which case the term add-one smoothing [ 2 ] [ 3 ] is also used ...
In probability theory and directional statistics, a wrapped asymmetric Laplace distribution is a wrapped probability distribution that results from the "wrapping" of the asymmetric Laplace distribution around the unit circle. For the symmetric case (asymmetry parameter κ = 1), the
Bayesian probability Laplace's equation Laplacian Laplace transform Inverse Laplace transform Laplace distribution Laplace's demon Young–Laplace equation Laplace number Laplace limit Laplace invariant Laplace principle Laplace's principle of insufficient reason Laplace's method Laplace force Laplace filter Laplace functional Laplacian matrix ...