order probability distributions (cf. [[Probability distribution|Probability distribution]]) $ P = \{ p _ {1} \dots p _ {K} \} $,
between the source probability distribution $ P $
6 KB (919 words) - 22:11, 5 June 2020
...formed data. Such an approach may be easily carried out, and an asymptotic theory associated with other parameters is useful. See [[#References|[a1]]] and [[
...o [[Outlier|Outlier]]). Further, in certain situations, the usual limiting theory based on knowing $ \lambda $
9 KB (1,146 words) - 06:29, 30 May 2020
...n in the sense of the classical theory of functions, and is defined in the theory of generalized functions as a singular [[Generalized function|generalized f
...<0$, $h(x)=1$ for $x>0$ (the value at zero does not matter; as usual for a distribution it suffices for it to be defined apart from a set of measure zero).
2 KB (390 words) - 22:12, 31 December 2018
''neutron age theory''
...r example, are not permitted). The assumption which underlies neutron flow theory is that the slowing down neutrons lose their energy continuously rather tha
3 KB (514 words) - 11:47, 5 July 2014
...precisely, suppose that the random variables $X_1,\dots,X_n$ have a joint distribution in $\R^n$, and let $X^*_{1;3\dots n}$, $X^*_{2;3\dots n}$ be the best linea
[[Student distribution|Student distribution]] with $N-n$ degrees of freedom.
4 KB (537 words) - 20:05, 6 April 2012
which satisfies (1) and is such that the distribution function of $ \mathbf w _ {n} $
converges monotone to the distribution function of $ \mathbf w _ {n} ^ {0} $
18 KB (2,750 words) - 19:29, 16 January 2024
...ounters not the probability integral, but the [[Normal distribution|normal distribution]] function
having the normal distribution with mathematical expectation 0 and variance $ \sigma ^ {2} $,
4 KB (598 words) - 19:23, 11 January 2024
...ntial equation which is satisfied by the [[Potential|potential]] of a mass distribution inside domains occupied by the masses creating this potential. For the [[Ne
where $\rho=\rho(x_1,\dots,x_n)$ is the density of the mass distribution, $\sigma(S^n)=n\pi^{n/2}/\Gamma(n/2+1)$ is the area of the unit sphere $S^n
2 KB (375 words) - 06:54, 27 August 2014
...gence]] in order to study the [[Convergence in distribution|convergence in distribution]] of stochastic processes with jumps.
...ed random variables (cf. [[Random variable|Random variable]]) converges in distribution if and only if their finite-dimensional distributions converge and the laws
4 KB (518 words) - 08:14, 6 June 2020
...sity (cf. [[Density of a probability distribution|Density of a probability distribution]]) of an observable random vector $ X = ( X _ {1} \dots X _ {n} ) $
Property (*) of the uniform distribution for $ R $
4 KB (582 words) - 08:05, 6 June 2020
...or constructing estimators of unknown parameters in statistical estimation theory.
with distribution $ {\mathsf P} _ \theta $
6 KB (728 words) - 17:20, 6 January 2024
be random variables whose joint distribution function $ F ( x , \theta ) $
is used with distribution function $ G ( t , \theta ) $,
8 KB (1,137 words) - 07:29, 24 March 2023
...10/b01511031.png" /> is absolutely continuous, and the density of the mass
distribution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...cyclopediaofmath.org/legacyimages/b/b015/b015110/b01511046.png" />, a mass
distribution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
21 KB (2,931 words) - 16:56, 7 February 2011
...This part may be considered as the first serious study ever of probability theory. The book was published in 1713 by N. Bernoulli (a nephew of Jacob Bernoull
...lusively based on a study of the decrease of probabilities in the binomial distribution as one moves away from the most probable value, was accompanied by an inequ
4 KB (524 words) - 10:58, 29 May 2020
has a definite probability distribution whose mathematical expectation is a function of $ x $:
In probability theory, the problem of regression is solved in case the values of the regression v
10 KB (1,524 words) - 08:10, 6 June 2020
...91 : ~/encyclopedia/old_files/data/D031/D.0301110 Density of a probability distribution,
The derivative of the [[Distribution function|distribution function]] corresponding to an absolutely-continuous probability measure.
6 KB (898 words) - 17:32, 5 June 2020
A conjecture on the distribution of [[prime number]]s.
...">[2]</TD> <TD valign="top"> Richard K. Guy, "Unsolved problems in number theory" (3rd ed.) Springer-Verlag (2004) {{ISBN|0-387-20860-7}} {{ZBL|1058.11001}}
1 KB (161 words) - 19:26, 14 November 2023
The [[Probability distribution|probability distribution]] of a [[Brownian motion|Brownian motion]] $ \{ {B ( t ) } : {t \geq 0 }
...e (cf. also [[Constructive quantum field theory|Constructive quantum field theory]]) that can be supported by the space $ C = C [ 0, \infty ) $
5 KB (792 words) - 08:29, 6 June 2020
A proposition from the theory of statistical estimation on which a method for the improvement of unbiased
...er a sufficient statistic. That is how the best unbiased estimator for the distribution function of the normal law is constructed in the following example, which i
7 KB (1,026 words) - 19:47, 16 January 2024
is called weakly convergent to a distribution $ P $
Weak convergence is a basic type of convergence considered in probability theory. It is usually denoted by the sign $ \Rightarrow $.
6 KB (936 words) - 19:36, 5 June 2020