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...stic processes whose associated [[probability distribution]]s are [[stable distributions]].<ref name=essentials/> Examples of stable processes include the [[Wiener process]], or [[Brownian motion]], whose ass ...

The '''Mittag-Leffler distributions''' are two families of [[probability distributions]] on the half-line <math>[0,\infty)</math>. They are parametrized by a real ==First family of Mittag-Leffler distributions== ...

...They are the discrete analogue of [[stable distribution|continuous-stable distributions]]. Discrete-stable distributions have been used in numerous fields, in particular in [[scale-free networks]] ...

...s functions or probability density functions respectively. Many well known distributions have simple convolutions. The following is a list of these convolutions. Ea ...lace of <math>X_i</math> and <math>Y</math> the names of the corresponding distributions and their parameters have been indicated. ...

...stable processes have been proposed for overcoming this limitation of the stable distribution. ...[volatility clustering]]. In the GARCH model, the innovation (or residual) distributions are assumed to be a standard normal distribution, despite the fact that thi ...

| name = Geometric stable ...The [[Mittag-Leffler distribution]] is also a special case of a geometric stable distribution.<ref>{{cite journal|author=D.O. Cahoy|author2=V.V. Uhaikin|aut ...

...|325px|Symmetric stable distributions]]<br /><small>Symmetric ''α''-stable distributions with unit scale factor; ''α''=1.5 (blue line) represents the Holtsmark dist ...= [[File:Levy distributionCDF.svg|325px|CDF's for symmetric ''α''-stable distributions; ''α''=3/2 represents the Holtsmark distribution]] ...

| name = multivariate stable ...stable.png|220px]]<br/> <small>Heatmap showing a Multivariate (bivariate) stable distribution with&nbsp;''&alpha;''&nbsp;=&nbsp;1.1</small> ...

...mmetric multivariate Laplace distribution variables are asymmetric Laplace distributions.<ref name=kotz>{{cite book|title=The Laplace Distribution and Generalizatio ...me=fit>{{cite journal|title=Goodness-of-fit tests for multivariate Laplace distributions|author=Fragiadakis, Konstantinos & Meintanis, Simos G.|journal=Mathematical ...

{{Short description|Definition and first properties of the Poisson-Dirichlet distributions}} ...bability theory]], '''Poisson-Dirichlet distributions''' are [[probability distributions]] on the set of nonnegative, non-increasing sequences with sum 1, depending ...

...distributions.jpg|thumb|Relationships among some of univariate probability distributions are illustrated with connected lines. dashed lines means approximate relati ...pages=2719–21 | title=ProbOnto: ontology and knowledge base of probability distributions | year=2016 | journal=Bioinformatics | last1 = Swat | first1 = MJ | last2 = ...

Mixed binomial processes are stable under restrictions in the sense that if <math> \xi </math> is a mixed bino ...nly distributions in the canonical non-negative [[power series]] family of distributions to possess this property and include the [[Poisson distribution]], [[negati ...

...ver, for example the normal and log-normal distributions, still continuous distributions exist that are not covered.<ref>{{Cite book |last1=Smith |first1=Richard L. * [[Stable distribution]] ...

...1972)<ref>Press SJ (1972) Estimation in univariate and multivariate stable distributions. Journal of the American Statistical Association. 67:842–846</ref> for [[pa ...rgő (1984a),<ref>Csörgő S (1984a) Adaptive estimation of the parameters of stable laws. In P. Revesz (ed) Colloquia Mathematica Societatis Janos Bolyai 36. L ...

...invariant. Arthur later found the '''invariant trace formula''' and the '''stable trace formula''' which are more suitable for applications. The '''simple tr ...sion of the trace formula {{harv|Arthur|1983}} asserts the equality of two distributions on {{math|''G''('''A''')}}: ...

{{Short description|Family of distributions that generalize the multivariate normal distribution}} ...icularly for spherical distributions (which are defined below). Elliptical distributions are also used in [[robust statistics]] to evaluate proposed multivariate-st ...

...x''&nbsp;=&nbsp;''m'', the asymmetric Laplace consists of two exponential distributions of unequal scale back to back about ''x''&nbsp;=&nbsp;''m'', adjusted to as ...st2=Kozubowski |first2=Tomasz J. |year=2004 |title=New Families of Wrapped Distributions for Modeling Skew Circular Data |journal=Communications in Statistics – The ...

...ing some support condition. A [[convolution (mathematics)|convolution]] of distributions is again a distribution and thus they form the [[Hopf algebra]] on ''G'', d == Distributions on an algebraic group == ...

...or [[central tendency]], and together they are the most used properties of distributions. ...g the measured results. One may assume that the quantity being measured is stable, and that the variation between measurements is due to [[observational erro ...

...s no one left, but if we model the number of people it is likely to remain stable for a long period of time before it eventually collapses. ...<math>\{ \operatorname{P}_x \mid x \in \mathcal{X} \}</math> the family of distributions where <math>\operatorname{P}_x</math> has original condition <math>Y_0 = x ...