to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after...

multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate...

geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced...

discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution under...

probability theory, the stable count distribution is the conjugate prior of a one-sided stable distribution. This distribution was discovered by Stephen...

case of the inverse-gamma distribution. It is a stable distribution. The probability density function of the Lévy distribution over the domain x ≥ μ {\displaystyle...

the few stable distributions with a probability density function that can be expressed analytically, the others being the normal distribution and the...

theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...

Mandelbrot first used the stable (or α {\displaystyle \alpha } -stable) distribution to model the empirical distributions which have the skewness and...

X ∼ GeometricStable ( 2 , 0 , λ , 0 ) {\displaystyle X\sim {\textrm {GeometricStable}}(2,0,\lambda ,0)} (geometric stable distribution) then X ∼ Laplace...

The Johnson SU distribution The Landau distribution The Laplace distribution The Lévy skew alpha-stable distribution or stable distribution is a family of...

stationary (marginal) distribution, although in probability and statistics the term has a rather different meaning: see stable distribution. Crudely stated...

such as mean or variance, are undefined. The distribution is a particular case of stable distribution. The probability density function, as written originally...

statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

[pwasɔ̃]). It plays an important role for discrete-stable distributions. Under a Poisson distribution with the expectation of λ events in a given interval...

t-distribution; The family of stable distributions, excepting the special case of the normal distribution within that family. Some stable distributions...

is a random walk in which the step-lengths have a stable distribution, a probability distribution that is heavy-tailed. When defined as a walk in a space...

stable process is a type of stochastic process. It includes stochastic processes whose associated probability distributions are stable distributions....

statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or...

same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be "stable distributions"....

Named joint distributions that arise frequently in statistics include the multivariate normal distribution, the multivariate stable distribution, the multinomial...

Laplace distribution, including the special case of μ = 0 {\displaystyle {\boldsymbol {\mu }}=\mathbf {0} } , is an example of a geometric stable distribution...

1 < p < 2, gamma distribution, p = 2, positive stable distributions, 2 < p < 3, Inverse Gaussian distribution, p = 3, positive stable distributions, p > 3, and...

b_{n}.} Distributions Ξ which can arise in this way are called stable. Clearly, the normal distribution is stable, but there are also other stable distributions...

Frechet distribution is a max stable distribution The negative of a random variable having a Frechet distribution is a min stable distribution Type-2 Gumbel...

a d-dimensional vector with entries chosen independently from a stable distribution and b {\displaystyle b} is a real number chosen uniformly from the...

shortcoming of the normal distribution model and have proposed that fat-tailed distributions such as the stable distributions govern asset returns frequently...

local time, stable distributions and characteristic functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribution, the Lévy...

(one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index...

value distribution is a special case of a max-stable distribution, and is a transformation of a min-stable distribution. The GEV distribution is widely...