One of the basic terms in classical statistics and [[Probability theory|probability theory]]. In the axiomatic approach it is defined as any decomposition of t
[[Category:Probability and statistics]]
649 bytes (94 words) - 07:34, 2 November 2014
...iable $X$. The quantiles $K_{1/4}$ and $K_{3/4}$ are called the quartiles, and $K_{0.1},\ldots,K_{0.9}$, the deciles. The values of the quantiles for suit
The quartiles of the normal distribution $\Phi$ are $K_{1/4}=-0.67$ and $K_{3/4}=0.67$.
2 KB (269 words) - 16:40, 5 August 2014
...increasing order, then a point $x_m$ is called a mode if $p_m \ge p_{m-1}$ and $p_m \ge p_{m+1}$.
...with respect to some point $a$, the mode is equal to $a$ and to the median and to the mathematical expectation, if the latter exists.
2 KB (243 words) - 20:49, 14 December 2015
* In probability and statistics: the way to describe probability of random variables taking certain values, see [[Distribution function|Dist
* In differential geometry and topology: [[Distribution of tangent subspaces]].
415 bytes (50 words) - 07:47, 3 May 2012
Any [[probability distribution]] having support on some (linear) manifold of dimension smalle
...to a measure of infinite total mass, which is still being manipulated as a probability distribution. Cf. also [[Improper distribution|Improper distribution]].
1 KB (156 words) - 19:24, 26 October 2014
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...m variables subject to the same absolutely-continuous probability law with probability density $ p( x) $.
4 KB (604 words) - 08:25, 6 June 2020
...sure]] on the real line whose density is zero outside the interval $(0,1)$ and is $(\sqrt{x(1-x)})^{-1}/\pi$ if $0<x<1$. The corresponding distribution fu
...wal theory (cf. [[Arcsine law|Arcsine law]]), and are used in mathematical statistics as special cases of the beta-distribution.
2 KB (226 words) - 12:50, 11 October 2014
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A continuous [[Probability distribution|probability distribution]] with density
3 KB (364 words) - 15:52, 7 June 2020
...ned as the discrete distribution that assigns to every value $ X_{k} $ the probability $ \dfrac{1}{n} $. The empirical distribution function $ F_{n} $ is the step
\dfrac{k}{n}, & \text{if} ~ X_{(k)} < x \leq X_{(k + 1)} ~ \text{and} ~ 1 \leq k \leq n - 1; \\
5 KB (778 words) - 04:08, 22 June 2017
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...f probability mass outside a given interval to within this interval. Let a probability distribution on the line be given by a distribution function $ F $.
4 KB (545 words) - 14:56, 7 June 2020
...},\dots,X_{(n)}$, that is, of the quantity $X_{(k+1)}$ if $n=2k+1$ is odd, and of $[X_{(k)}+X_{(k+1)}]/2$ if $n=2k$ is even.
|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
...statistical test]] for testing the hypothesis $H_0$ that a one-dimensional probability density is symmetric about zero.
...hypothesis of symmetry $H_0$ be that the probability density $p(x)$ of the probability law of independent random variables $X_1,\ldots,X_n$ is symmetric about zer
1 KB (238 words) - 16:19, 19 April 2014
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A probability distribution on the simplex
2 KB (306 words) - 08:57, 8 April 2023
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...stributions (cf. [[Discrete distribution|Discrete distribution]]) given by probability vectors $ p = ( p _ {1} \dots p _ {n} ) $,
2 KB (316 words) - 22:15, 5 June 2020
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of dispersion for a [[Probability distribution|probability distribution]]. For a continuously-distributed symmetric random variable $
2 KB (234 words) - 08:07, 6 June 2020
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containing with given probability $ \gamma $
7 KB (924 words) - 10:30, 16 July 2021
...sure on $S$ such that $\operatorname P(\Omega)=1$ (a [[Probability measure|probability measure]]).
...terization in different terms (see [[Separable process|Separable process]] and also {{Cite|P}}).
8 KB (1,003 words) - 21:59, 21 November 2018
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...matorstrong consistency" for a sequence of estimators that converges with probability 1 to the value being evaluated.
4 KB (501 words) - 17:46, 4 June 2020
...= 20 : ~/encyclopedia/old_files/data/M064/M.0604610 Moments, method of (in probability theory)
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4 KB (609 words) - 16:25, 6 January 2024
...ferences obtained using it do not depend on the particular null-hypothesis probability distribution of the observable random variables on the basis of which one w
See also [[Non-parametric methods in statistics]]; [[Kolmogorov–Smirnov test]].
2 KB (247 words) - 09:06, 10 April 2023