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...aracterization (mathematics)|characterization]] theorems of [[mathematical statistics]]. It is easy to see that if the random variables <math>\xi</math>&nbsp; an ...ization of the Kac–Bernstein theorem is the [[Darmois–Skitovich theorem]], in which instead of sum and difference linear forms from ''n'' independent ran ...

...y order. It is a special case of the [[Burkholder-Davis-Gundy inequality]] in the case of discrete-time martingales. ...fonctions indépendantes. ''Fund. Math.'', 28:60&ndash;90, 1937. Reprinted in Józef Marcinkiewicz, ''Collected papers'', edited by Antoni Zygmund, Panstw ...

...-dimensional hypersphere]] all lie on the same "half" of the hypersphere. In other words, one seeks the probability that there is some [[Half-space (geo |last = Wendel|first = James G.|title = A Problem in Geometric Probability|journal = Math. Scand.|volume = 11|year = 1962|pages ...

{{Short description|Statement in probability theory}} In the [[mathematics|mathematical]] [[probability theory|theory of probability ...

...ction, a space, etc. – is the only one that possesses properties specified in the theorem. A '''characterization of a probability distribution''' accordi ...bles <math> X \in\mathcal{A}</math> and their images <math> Y=\mathbf{F}X \in \mathcal{B} </math>, obtained by means of a specially chosen mapping <math> ...

In [[statistics]], the '''matrix variate Dirichlet distribution''' is a generalization of t == Theorems == ...

{{Short description|Statistics named for Richard von Mises}} ...r "[[bias of an estimator|unbiased]]") introduced by [[Wassily Hoeffding]] in 1948.<ref>{{harvtxt|Hoeffding|1948}}</ref> A V-statistic is a statistical ...

...characterization of the gamma distribution|journal=Annals of Mathematical Statistics|volume=26|year=1955|issue= 2|pages=319–324|doi-access=free}}</ref> [[Category:Probability theorems]] ...

In [[statistics]], the '''matrix variate beta distribution''' is a generalization of the [[ == Theorems == ...

In the mathematical theory of probability, the '''Heyde theorem'''&nbsp;is the ...Yu. V. Linnik, and C. R. Rao, ''Characterization Problems in Mathematical Statistics'', Wiley, New York (1973). ...

...proved independently by [[Georges Darmois|G. Darmois]] and V. P. Skitovich in 1953.<ref name=darmois>{{cite journal ...ois–Skitovich theorem is a generalization of the [[Kac–Bernstein theorem]] in which the [[normal distribution]] (the Gaussian distribution) is character ...

...'Hájek–Le Cam convolution theorem''' states that any [[regular estimator]] in a [[parametric model]] is asymptotically equivalent to a sum of two [[indep ...model]], and ''q''(''θ''): Θ&nbsp;→&nbsp;ℝ^''m'' be a parameter in this model (typically a parameter is just one of the components of vector&n ...

...ilities differ, though with a variance estimate that has an upward [[Bias (statistics)|bias]]. ...-based confidence interval estimation for tail-area FDR |journal=Frontiers in Genetics |volume=4 |issue=179 |pages=1–11 |pmc=3775454 |doi=10.3389/fgene.2 ...

...resentation for [[Wiener functional]]s. The representation has application in finding [[large deviation theory|large deviation]] asymptotics. ...he result was generalized to infinite-dimensional [[Brownian motion]]s and in 2009<ref>{{cite journal|first1=Xicheng|last1=Zhang|publisher=Duke Universit ...

...alid for large finite sample sizes too.<ref>Höpfner, R. (2014), Asymptotic Statistics, Walter de Gruyter. 286 pag. {{ISBN|3110250241}}, {{ISBN|978-3110250244}}</ ...rap|''n'' → ∞}}}}.<ref name=ONE>A. DasGupta (2008), ''Asymptotic Theory of Statistics and Probability'', Springer. {{ISBN|0387759700}}, {{ISBN|978-0387759708}}</ ...

{{Short description|Theorem in probability theory}} ...named for Russian mathematician [[Dmitrii Abramovich Raikov]], is a result in [[probability theory]]. It is well known that if each of two [[independence ...

...for goodness of fit for symmetric random variables. Australian Journal of Statistics. 14:172-181</ref> for [[goodness-of-fit]] testing. ...Journal. 50:1-41</ref> Ushakov (1999)<ref>Ushakov N (1999) Selected Topics in Characteristic Functions. VSP, Utrecht.</ref> and Prakasa Rao (1987)<ref>Pr ...

{{short description|Result concerning the holomorphic extensions In several complex variables}} ...1}}</ref> Many generalizations and similar results exist, and are known as theorems of Ohsawa–Takegoshi type. ...

{{ about|the theorem in Markov probability theory|the theorem in electrical engineering|Foster's reactance theorem}} ...itive recurrent Markov chains exhibit a notion of "[[Lyapunov stability]]" in terms of returning to any state while starting from it within a finite time ...

...[[Ivan Rival]] and Bill Sands in 1981. It was proved by [[Lawrence Shepp]] in ...epp|1982}}. An extension was given by [[Peter C. Fishburn|Peter Fishburn]] in {{harvtxt|Fishburn|1984}}. ...