''in probability theory''
...]] or the [[Density of a probability distribution|density of a probability distribution]].
337 bytes (43 words) - 17:03, 7 February 2011
[[Category:Distribution theory]]
...respectively, is such a mixture. The distribution function of a continuous distribution is a continuous function. The absolutely-continuous distributions occupy a
6 KB (843 words) - 11:58, 20 October 2012
The probability distribution concentrated on $(0,\infty)$ with density
...mber $\mu>0$ are parameters. The [[characteristic function]] of the Erlang distribution has the form
2 KB (279 words) - 19:37, 4 December 2016
[[Category:Distribution theory]]
...al $(0,1)$ and is $(\sqrt{x(1-x)})^{-1}/\pi$ if $0<x<1$. The corresponding distribution function is equal to $(2/\pi)\arcsin\sqrt x$ for $0\leq x\leq1$.
2 KB (226 words) - 12:50, 11 October 2014
$#C+1 = 12 : ~/encyclopedia/old_files/data/G044/G.0404230 Geometric distribution
[[Category:Distribution theory]]
1 KB (202 words) - 19:41, 5 June 2020
$#C+1 = 10 : ~/encyclopedia/old_files/data/R077/R.0707730 Rayleigh distribution
A continuous [[Probability distribution|probability distribution]] with density
3 KB (338 words) - 12:55, 17 March 2023
$#C+1 = 9 : ~/encyclopedia/old_files/data/L060/L.0600780 Logistic distribution
A probability distribution with distribution function $ \psi ( a x + b ) $,
2 KB (254 words) - 17:36, 12 January 2021
$#C+1 = 24 : ~/encyclopedia/old_files/data/T094/T.0904360 Truncated distribution
...in this interval. Let a probability distribution on the line be given by a distribution function $ F $.
4 KB (545 words) - 14:56, 7 June 2020
...of the hypothetical distribution. The straight line represents the normal distribution function with average 100 and standard deviation 8.
...>[1]</TD> <TD valign="top"> N. Arley, K.R. Buch, "Introduction to the theory of probability and statistics" , Wiley (1950)</TD></TR><TR><TD valign="top
1 KB (206 words) - 19:52, 3 May 2023
A continuous probability distribution with density
...s a discontinuity at $x=\beta$. The characteristic function of the Laplace distribution with parameters $\alpha$ and $\beta$ is
2 KB (326 words) - 07:53, 20 August 2014
$#C+1 = 16 : ~/encyclopedia/old_files/data/D033/D.0303060 Discrete distribution
[[Category:Distribution theory]]
2 KB (315 words) - 19:35, 5 June 2020
$#C+1 = 17 : ~/encyclopedia/old_files/data/M063/M.0603130 Maxwell distribution
The [[Probability distribution|probability distribution]] with probability density
3 KB (351 words) - 11:10, 9 April 2023
$#C+1 = 20 : ~/encyclopedia/old_files/data/M062/M.0602340 Marginal distribution
...iven distribution. Thus the marginal distribution is the projection of the distribution of the random vector $ X= ( X _ {1} \dots X _ {n} ) $
2 KB (343 words) - 07:40, 14 January 2024
$#C+1 = 36 : ~/encyclopedia/old_files/data/N066/N.0606180 Negative binomial distribution
A [[Probability distribution|probability distribution]] of a random variable $ X $
4 KB (583 words) - 08:02, 6 June 2020
...distribution determined by the simple hypothesis is called the hypothesis distribution. E.g., if one observes a random variable $X$, then the statement "X is sub
.../TD> <TD valign="top"> A.M. Mood, F.A. Graybill, "Introduction to the theory of statistics" , McGraw-Hill (1963) pp. §12.2</TD></TR></table>
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A [[Probability distribution|probability distribution]] on $\mathbf R^n$ concentrated on a set of [[Lebesgue measure|Lebesgue mea
...uivalent to the following: A distribution is singular if the corresponding distribution function is continuous and its set of growth points has Lebesgue measure ze
2 KB (359 words) - 18:13, 3 August 2014
$#C+1 = 29 : ~/encyclopedia/old_files/data/P071/P.0701750 Pascal distribution
A discrete [[Probability distribution|probability distribution]] of a random variable $ X $
3 KB (407 words) - 08:05, 6 June 2020
...18 : ~/encyclopedia/old_files/data/C022/C.0202100 \BQT Chi\AAhsquared\EQT distribution,
distribution''
4 KB (555 words) - 16:43, 4 June 2020
$#C+1 = 33 : ~/encyclopedia/old_files/data/C020/C.0200850 Cauchy distribution
[[Category:Distribution theory]]
4 KB (498 words) - 15:35, 4 June 2020
...eory]] characterising those [[additive function]]s that possess a limiting distribution.
==Limiting distribution==
2 KB (230 words) - 12:04, 23 November 2023
...o be contrasted with its unconditional or [[A priori distribution|a priori distribution]].
...the conditional density of $X$ when $\Theta=\theta$; then the a posteriori distribution of $\Theta$ for a given $X=x$, according to the [[Bayes formula|Bayes formu
2 KB (248 words) - 21:34, 1 January 2019
...of]]; [[Least squares, method of|Least squares, method of]]). Thus, in the theory of (observational) errors, developed by Gauss for problems in astronomy and
...ribution appears as the limit form of the [[Binomial distribution|binomial distribution]] (with $p=1/2$) had been discovered by A. de Moivre.
2 KB (312 words) - 16:10, 19 August 2014
$#C+1 = 25 : ~/encyclopedia/old_files/data/W098/W.0908040 Wishart distribution
...ution]]. Let the results of observations have a $ p $-dimensional normal distribution $ N( \mu , \Sigma ) $
3 KB (370 words) - 01:20, 19 January 2022
...discrete distributions: If the values $x_k$ of a random variable $X$ with distribution $p_k = \mathsf{P}(X = x_k)$ are arranged in increasing order, then a point
...and mathematical statistics are the unimodal distributions (cf. [[Unimodal distribution]]). Along with the [[mathematical expectation]] and the [[Median (in statis
2 KB (243 words) - 20:49, 14 December 2015
''$F$-distribution, Fisher–Snedecor distribution, Snedecor distribution''
A continuous probability distribution concentrated on $(0,\infty)$ with density
7 KB (873 words) - 07:45, 27 January 2024
The density of a [[Conditional distribution|conditional distribution]]. Let $ ( \Omega , {\mathcal A} , {\mathsf P} ) $
be the conditional distribution of $ X $
2 KB (296 words) - 17:46, 4 June 2020
...value|Exceptional value]]; [[Value-distribution theory|Value-distribution theory]].
...p">[3]</TD> <TD valign="top"> A.A. Gol'dberg, I.V. Ostrovskii, "Value distribution of meromorphic functions" , Moscow (1970) (In Russian)</TD></TR></table>
3 KB (516 words) - 17:32, 5 June 2020
$#C+1 = 40 : ~/encyclopedia/old_files/data/M065/M.0605330 Multinomial distribution,
''polynomial distribution''
4 KB (522 words) - 13:11, 6 January 2024
$#C+1 = 16 : ~/encyclopedia/old_files/data/D032/D.0302840 Dirichlet distribution
A probability distribution on the simplex
2 KB (306 words) - 08:57, 8 April 2023
...de with limiting forms of the [[Hypergeometric distribution|hypergeometric distribution]]. Pearson curves are classified in accordance with the character of the ro
...Pearson curves consists of 12 types plus the [[Normal distribution|normal distribution]]. Many very important distributions in mathematical statistics may be obta
6 KB (779 words) - 07:20, 24 March 2023
Khinchin's theorem on the factorization of distributions: Any probability distribution $P$ admits (in the convolution semi-group of probability distributions) a f
...ite or countable set of indecomposable distributions (cf. [[Indecomposable distribution]]). The factorization (1) is not unique, in general.
2 KB (326 words) - 16:26, 9 April 2016
$#C+1 = 15 : ~/encyclopedia/old_files/data/J054/J.0504260 Joint distribution
A general term referring to the distribution of several random variables defined on the same probability space. Let $
2 KB (319 words) - 22:14, 5 June 2020
$#C+1 = 34 : ~/encyclopedia/old_files/data/U095/U.0905330 Unimodal distribution,
''single-peak distribution''
5 KB (663 words) - 07:36, 10 April 2023
distribution''
A continuous probability distribution concentrated on the positive semi-axis $ 0 < x < \infty $
4 KB (556 words) - 18:53, 24 January 2024
$#C+1 = 58 : ~/encyclopedia/old_files/data/C024/C.0204480 Conditional distribution
...or each fixed elementary event is a [[Probability distribution|probability distribution]] and for each fixed Borel set is a [[Conditional probability|conditional p
4 KB (599 words) - 17:46, 4 June 2020
A continuous probability distribution concentrated on the positive semi-axis $ 0 < x < \infty $
The corresponding distribution function for $ x \leq 0 $
5 KB (610 words) - 19:21, 10 April 2024
''domain of attraction of a stable distribution''
[[Category:Distribution theory]]
3 KB (488 words) - 20:56, 1 January 2019
$#C+1 = 38 : ~/encyclopedia/old_files/data/L057/L.0507640 Lattice distribution
A discrete probability distribution concentrated on a set of points of the form $ a + nh $,
4 KB (622 words) - 22:15, 5 June 2020
[[Category:Distribution theory]]
...tion]], the uniform distribution appears in probability theory as an exact distribution in some problems and as a limit in others.
6 KB (911 words) - 12:00, 22 December 2019
...variable $X$ is being tested, using a test based on a statistic $T(X)$ the distribution function of which — provided $H_0$ is true — is $G(t)$. If the critical
...><TR><TD valign="top">[2]</TD> <TD valign="top"> J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967)</TD></TR></table>
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''sample distribution''
...s to every value $ X_{k} $ the probability $ \dfrac{1}{n} $. The empirical distribution function $ F_{n} $ is the step-function with steps of multiples of $ \dfrac
5 KB (778 words) - 04:08, 22 June 2017
be a random variable having a continuous and strictly increasing distribution function $ F $.
has a uniform distribution on the interval $ [ 0 , 1 ] $,
4 KB (562 words) - 20:33, 16 January 2024
...tatistical problem connected with the study of other parameters of a given distribution. More precisely, for a realization of a random variable $ X $,
...to make a statistical inference not depending on these parameters. In the theory of statistical hypothesis testing one often achieves this by narrowing the
2 KB (341 words) - 08:03, 6 June 2020
...al distribution]]. It is used as a certain measure of the deviation of the distribution in question from the normal one. The excess $ \gamma _ {2} $
is the second Pearson coefficient (cf. [[Pearson distribution|Pearson distribution]]), and $ \mu _ {2} $
4 KB (594 words) - 17:18, 6 January 2024
distribution''
The [[Probability distribution|probability distribution]] of the random variable
3 KB (396 words) - 20:47, 22 January 2024
''in probability theory and mathematical statistics''
Theorems that establish a connection between the type of the distribution of random variables or random vectors and certain general properties of fun
3 KB (414 words) - 16:43, 4 June 2020
$#C+1 = 36 : ~/encyclopedia/old_files/data/H048/H.0408430 Hypergeometric distribution
The probability distribution defined by the formula
4 KB (602 words) - 22:11, 5 June 2020
...h that the distributions of $X_2$ and $BX_1+A$ coincide. The corresponding distribution functions are then connected by the relation
Thus the set of distribution functions decomposes into mutually disjoint types. For example, all normal
4 KB (649 words) - 14:15, 17 April 2014
...yclopedia/old_files/data/M064/M.0604610 Moments, method of (in probability theory)
A method for determining a [[Probability distribution|probability distribution]] by its moments (cf. [[Moment|Moment]]). Theoretically the method of momen
4 KB (609 words) - 16:25, 6 January 2024
$#C+1 = 42 : ~/encyclopedia/old_files/data/I052/I.0502550 Involutive distribution
A $ p $-dimensional distribution (or a differential system of dimension $ p $)
3 KB (378 words) - 10:11, 21 March 2022