statistics is [[#References|[a1]]]:
$ A \in {\mathcal X} $.
9 KB (1,249 words) - 08:27, 6 June 2020
The large sample study of test statistics in a given hypotheses testing problem is commonly based on the following conce
.... Assume that large values of a test statistic (cf. [[Test statistics|Test statistics]]) $ T _ {n} = T _ {n} ( \mathbf x ) $
5 KB (708 words) - 23:24, 11 May 2020
$#C+1 = 27 : ~/encyclopedia/old_files/data/C021/C.0201760 Characterization theorems
''in probability theory and mathematical statistics''
3 KB (414 words) - 16:43, 4 June 2020
A member of the series of order statistics (also called [[variational series]]) based on the results of observations.
in an $ n $-
12 KB (1,803 words) - 09:08, 10 April 2023
$#C+1 = 39 : ~/encyclopedia/old_files/data/B016/B.0106850 Boltzmann statistics
...f particles of an ideal gas (since they do not interact) is not considered in the phase space of all particles (the $ \Gamma $-
5 KB (797 words) - 10:59, 29 May 2020
[[Category:Limit theorems]]
.../www.encyclopediaofmath.org/legacyimages/e/e035/e035060/e03506017.png" />. In particular, the first terms of the expansion have the form
6 KB (866 words) - 11:09, 12 May 2012
$#C+1 = 20 : ~/encyclopedia/old_files/data/M064/M.0604610 Moments, method of (in probability theory)
...ents in the proof of limit theorems in probability theory and mathematical statistics is based on the correspondence between moments and the convergence of distr
4 KB (609 words) - 16:25, 6 January 2024
...a sample space, $S$ is a $\sigma$-algebra of subsets of $\Omega$ specified in some way and $\operatorname P$ is a measure on $S$ such that $\operatorname
..., usually formulated as separability but also admitting a characterization in different terms (see [[Separable process|Separable process]] and also {{Cit
8 KB (1,003 words) - 21:59, 21 November 2018
One of the methods in analytic number theory based on the study of statistics of the distribution of the zeros of the Riemann zeta-function
in the strip $ 0\leq \sigma \leq 1 $,
4 KB (642 words) - 13:03, 6 January 2024
$#C+1 = 38 : ~/encyclopedia/old_files/data/L060/L.0600160 Local limit theorems
''in probability theory''
6 KB (856 words) - 15:13, 18 March 2022
of the infinitesimal probabilities $ p ^ {a} ( \xi ^ {a} \in A ) $
in a suitable function space (space of paths)). Problems concerning the asympt
3 KB (451 words) - 20:13, 10 January 2024
In mathematical analysis, a distribution function is any function satisfying 1
...tep" distribution function (it has jumps at all the dyadic-rational points in $\left[ 0, 1 \right]$);
6 KB (864 words) - 13:51, 12 December 2013
''in probability theory''
in particular, $\Var(-X) = \Var X$.
7 KB (1,127 words) - 20:19, 27 January 2020
...) measures used in [[Ergodic theory|ergodic theory]] and mixing conditions in [[Probability theory|probability theory]] based on appropriate mixing coeff
...on disjoint index subsets. An essential feature of these coefficients is, in contrast to ergodic theory, that they provide uniform bounds of dependence
7 KB (1,086 words) - 06:27, 26 March 2023
[[Category:Limit theorems]]
in probability.
4 KB (604 words) - 20:08, 7 January 2024
...ibutions of random variables (cf. [[Random variable|Random variable]]) and in relation to the joint probability distribution (cf. [[Joint distribution|Jo
...ses, the normal distribution curve becomes more and more pointed. A change in $ a $
11 KB (1,515 words) - 08:03, 6 June 2020
taking values in a [[Measurable space|measurable space]] $ ( S, {\mathcal S} ) $.
} \# \left \{ {1 \leq i \leq n } : {X _ {i} \in C } \right \} , \quad C \in {\mathcal S}.
9 KB (1,327 words) - 19:37, 5 June 2020
...oment of a mass distribution. The first-order moment (a statistical moment in mechanics) of a random variable $ X $
the moment of inertia in mechanics). The value $ {\mathsf E} | X | ^ {k} $
7 KB (1,019 words) - 08:53, 21 January 2024
In the particular case $ a = - \infty $(
In (1) the mass concentrated outside $ [ a, b] $
4 KB (545 words) - 14:56, 7 June 2020
...of extraction of information is connected with reducing the indefiniteness in the knowledge of some object, and the natural numerical measure of indefini
...mation, transmission of|Information, transmission of]]). Often, especially in pure mathematical papers, the term "information theory" is used as a syno
7 KB (993 words) - 17:28, 7 February 2011