...nd identically distributed random variables $\xi _ { k }$ converges to the distribution of this functional of the Wiener process.
...)$ by finding the explicit distribution of $f ( X _ { n } )$, which is the distribution of $f ( w )$ by the invariance principle.
6 KB (857 words) - 21:45, 15 December 2020
The distribution among the numbers $1,\ldots,m-1$ of those values of $x$ for which the congr
$n>1$, is solvable (or unsolvable) in integers. Questions on the distribution of power residues and non-residues have been studied most fully in the case
4 KB (628 words) - 19:38, 19 December 2014
...unction|transition function]] if and only if there is a stationary initial distribution $ \mu ( A) $
is finite, then a stationary initial distribution always exists, independent of whether the process has discrete $ ( t= 0 ,
4 KB (641 words) - 07:59, 6 June 2020
A chain of equations (hierarchy) for the one-particle, two-particle, etc., distribution functions of a classical statistical system. The functions are defined as f
particle normalized distribution function which satisfies the [[Liouville-equation(2)|Liouville equation]]:
5 KB (743 words) - 10:59, 29 May 2020
...évy inequality]]). In mathematical statistics, to estimate the median of a distribution in terms of independent results of observations $X_1,\dots,X_n$ one uses a
|valign="top"|{{Ref|L}}|| M. Loève, "Probability theory" , Springer (1977) {{MR|0651017}} {{MR|0651018}} {{ZBL|0359.60001}}
1 KB (227 words) - 22:02, 30 November 2018
...lopedia/old_files/data/B017/B.0107390 Boundary value problems in potential theory
...sses. It follows, therefore, that the boundary value problems of potential theory are primarily boundary value problems for elliptic equations and systems (c
5 KB (673 words) - 06:29, 30 May 2020
...s of successive subsets [[#References|[a4]]], in which case the asymptotic distribution is determined by recursive application of polynomials. A tree-based method
...pace-efficient recursive procedure for estimating a quantile of an unknown distribution" ''SIAM J. Scient. Statist. Comp.'' , '''4''' (1983) pp. 706–711</TD><
2 KB (281 words) - 17:22, 7 February 2011
...(cf. also [[Density of a probability distribution|Density of a probability distribution]]), and there is much literature on its properties as a statistical estimat
...eedman, P. Diaconis, "On the histogram as a density estimator: $ L_2 $ theory" ''Z. Wahrsch. Verw. Geb.'' , '''57''' (1981) pp. 453–476</TD></TR></t
3 KB (376 words) - 00:30, 11 June 2013
[[Category:Distribution theory]]
of distribution functions (cf. [[Distribution function|Distribution function]]) of one-dimensional random variables such that:
7 KB (1,007 words) - 04:11, 6 June 2020
have a joint normal distribution, then these two coefficients coincide, since in this case
...ribution of the sample information coefficient leads to the problem of the distribution of the sample information. The analysis of the sample information as a meas
3 KB (440 words) - 19:51, 18 January 2024
''imputation (in the theory of games)''
A distribution of the overall gain of all players in a [[cooperative game]] which satisfie
764 bytes (121 words) - 18:18, 9 January 2016
...nce of the variables. To construct the corresponding test one computes the distribution of $ r _ {s} $
one can use tables of the exact distribution (see [[#References|[2]]], [[#References|[4]]]), and when $ n > 10 $
4 KB (638 words) - 09:15, 6 January 2024
In the theory of order statistics the best studied case is the one where the components
are independent random variables having the same distribution, as is assumed hereafter. If $ F ( u) $
12 KB (1,803 words) - 09:08, 10 April 2023
While the modern theory of [[Correlation|correlation]] and [[Regression|regression]] has its roots
...ave a bivariate normal distribution (cf. also [[Normal distribution|Normal distribution]]), $\rho$ is a parameter of the joint density function
4 KB (683 words) - 07:24, 24 March 2023
...rees are equally probable. Then the height of the random tree has the same distribution as $\max(\eta_0,\ldots,\eta_{2n})$ in the Bernoulli excursion. Explicitly:
...he theory of random graphs" J.H. Dshalalow (ed.) , ''Advances in Queueing Theory, Methods, and Open Problems'' , CRC (1995) pp. 45–78</TD></TR>
3 KB (458 words) - 17:54, 26 December 2017
be independent identically-distributed random variables whose distribution function belongs to the family $ H = \{ F ( x) \} $
of all continuous distribution functions on $ \mathbf R ^ {1} $,
7 KB (902 words) - 17:46, 4 June 2020
''in number theory''
...#References|[1]]] to establish criteria for [[Uniform distribution|uniform distribution]] (cf. [[Weyl criterion|Weyl criterion]]).
5 KB (759 words) - 08:29, 6 June 2020
Under various assumptions regarding the distribution of the $ x _ {i} $,
there are exact and approximate expressions for the distribution of the serial correlation coefficients, and of their moments. Serial correl
2 KB (327 words) - 08:24, 20 January 2024
...ite. The Fourier–Stieltjes transform is extensively applied in probability theory, where the non-decreasing function
is continuous on the left; it is called a distribution, and
3 KB (473 words) - 20:16, 16 January 2024
...ability distribution|Probability distribution]]). Suppose that an a priori distribution for $ \theta $
is chosen. One of the fundamental theorems in the asymptotic theory of Bayesian inference (cf. [[Bayesian approach|Bayesian approach]]) is conc
8 KB (1,171 words) - 10:58, 29 May 2020