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
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A probability distribution with distribution function $ \psi ( a x + b ) $,
2 KB (254 words) - 17:36, 12 January 2021
where $\sigma^2$ is the variance and $\mu$ is the mathematical expectation ($\mu$ must be positive). This expres
[[Category:Probability and statistics]]
500 bytes (77 words) - 19:25, 8 November 2014
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The continuous probability distribution, concentrated on the positive semi-axis $ ( 0, \infty ) $,
4 KB (555 words) - 16:43, 4 June 2020
...lection should be so effected that any group of $n$ elements is drawn with probability $n!\,(N-n)!/N!$. This rule of sampling is realized in determining the winni
...t the sampling rule is defined by a distribution function $F$, so that the probability of obtaining an experimental result comprised in a semi-interval $(a,b]$ is
3 KB (427 words) - 17:10, 30 December 2018
...t a random variable $X$ be subject to the binomial law with parameters $n$ and $\theta$, where $\theta$, $0<\theta<1$, is unknown. The statistic
...nt random variables subject to the same probability law, with a continuous probability density $f(x-\theta)$, $|x|<\infty$, $|\theta|<\infty$. The Pitman estimato
2 KB (258 words) - 09:41, 19 November 2018
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A theorem in the theory of statistical estimation giving a necessary and sufficient condition for a statistic $ T $
4 KB (516 words) - 19:38, 5 June 2020
...diaofmath.org/legacyimages/e/e035/e035060/e0350606.png" /> are independent and identically distributed),
is the density of the standard [[Normal distribution|normal distribution]], and
6 KB (866 words) - 11:09, 12 May 2012
...certainty values of formulas, so that the propagation rule generates upper and lower bounds for the conclusion from those on the premises.
...Q$ can be anything between $0$ and the minimum of the probabilities of $P$ and $Q$.
3 KB (515 words) - 13:25, 18 July 2014
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A continuous probability distribution concentrated on the positive semi-axis $ 0 < x < \infty $
4 KB (556 words) - 18:53, 24 January 2024
[[Probability distribution|probability distribution]] of a random variable $X$ which takes non-negative integer va
...are <math>M</math> "marked" and <math>N-M</math> "unmarked" elements, and if the sampling (without replacement) is performed until the number of "ma
3 KB (447 words) - 14:48, 5 June 2017
...straight line represents the normal distribution function with average 100 and standard deviation 8.
...> N. Arley, K.R. Buch, "Introduction to the theory of probability and statistics" , Wiley (1950)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">
1 KB (206 words) - 19:52, 3 May 2023
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A scalar characteristic of the pointedness of the graph of the probability density of a [[Unimodal distribution|unimodal distribution]]. It is used as
4 KB (594 words) - 17:18, 6 January 2024
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The probability distribution of the random variable
5 KB (724 words) - 14:55, 7 June 2020
''(in probability theory)''
...w, the most natural assumption is that $\rho$ and $\theta$ are independent and uniformly distributed in the interval $0\leq\rho\leq1$, $0\leq\theta\leq2\p
2 KB (374 words) - 10:24, 16 March 2023
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''in probability theory and mathematical statistics''
3 KB (414 words) - 16:43, 4 June 2020
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...atural generalization of a [[Binomial distribution|binomial distribution]] and coincides with the latter for $ k = 2 $.
4 KB (522 words) - 13:11, 6 January 2024
$#C+1 = 21 : ~/encyclopedia/old_files/data/S087/S.0807490 Statistics
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3 KB (407 words) - 16:24, 6 January 2024
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A member of the series of order statistics (also called [[variational series]]) based on the results of observations.
12 KB (1,803 words) - 09:08, 10 April 2023
$#C+1 = 39 : ~/encyclopedia/old_files/data/B016/B.0106850 Boltzmann statistics
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5 KB (797 words) - 10:59, 29 May 2020
...e construction of a set of approximate values of the unknown parameters of probability distributions.
in a Euclidean space and let the probability distribution of this vector belong to the parametric family of distribution
8 KB (1,101 words) - 11:37, 10 February 2020
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A discrete probability distribution concentrated on a set of points of the form $ a + nh $,
4 KB (622 words) - 22:15, 5 June 2020
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...bability density (cf. [[Density of a probability distribution|Density of a probability distribution]]) of an observable random vector $ X = ( X _ {1} \dots X _
4 KB (582 words) - 08:05, 6 June 2020
A numerical characteristic of the probability distribution of a random variable. In the most general setting, the mathema
...esgue integral|Lebesgue integral]] with respect to a [[Probability measure|probability measure]] $ {\mathsf P} $
7 KB (945 words) - 11:49, 10 February 2020
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s strategy is a decision rule (decision function), and the pay-off function of player $ I $
3 KB (461 words) - 08:23, 6 June 2020
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A statistic having a fixed probability distribution under some compound hypothesis.
3 KB (460 words) - 08:54, 6 January 2024
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A metric or pseudo-metric on the set of probability distributions, characterizing the "non-similarity" of the random phenomen
7 KB (1,010 words) - 22:12, 5 June 2020
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''for a family of probability distributions $ \{ {P _ \theta } : {\theta \in \Theta } \} $
9 KB (1,282 words) - 08:24, 6 June 2020
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A discrete [[Probability distribution|probability distribution]] of a random variable $ X $
3 KB (407 words) - 08:05, 6 June 2020
...function of a real variable $x$ taking at each $x$ the value equal to the probability of the inequality $X < x$.
...w +\infty} F(x) = 1$. (Sometimes a distribution function is defined as the probability of $X \le x$; it is then right-continuous.)
6 KB (864 words) - 13:51, 12 December 2013
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A numerical characteristic of a [[Probability distribution|probability distribution]]. The moment of order $ k $(
7 KB (1,019 words) - 08:53, 21 January 2024