$#C+1 = 23 : ~/encyclopedia/old_files/data/D110/D.1100030 De Haan theory
...riation, initiated in 1930 by the Yugoslav mathematician J. Karamata. This theory studies asymptotic relations of the form
5 KB (688 words) - 17:32, 5 June 2020
There are theorems for almost-prime numbers that generalize theorems on the distribution of prime numbers in the set of natural numbers. Several [[Additive problems
An example of a result on the distribution of almost-prime numbers generalizing the corresponding one on prime numbers
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[[Category:Distribution theory]]
...function]] of an [[Infinitely-divisible distribution|infinitely-divisible distribution]]:
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is the particle distribution function, while the index $ \alpha $
are related to the particle distribution function via
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The distribution of the fractional parts $\{\alpha_j\}$ of a sequence of real numbers $\alph
[[Weyl criterion|Weyl's criterion]] (see [[#References|[1]]]) for a distribution modulo one to be uniform: An infinite sequence of fractional parts $\{\alph
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...nction. Let $X_1,\ldots,X_n$ be independent random variables with the same distribution such that
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...ample is drawn from the population at random. From the view of probability theory, a "random" choice means that if the population contains $N$ elements and
...pulation. In so doing it is assumed that the sampling rule is defined by a distribution function $F$, so that the probability of obtaining an experimental result c
3 KB (427 words) - 17:10, 30 December 2018
$#C+1 = 74 : ~/encyclopedia/old_files/data/N067/N.0607460 Normal distribution
[[Category:Distribution theory]]
11 KB (1,515 words) - 08:03, 6 June 2020
...n]]). In (a1), $f$ is the density function of some [[Distribution function|distribution function]] $F$ having all moments $\alpha _ { k } = \int x ^ { k } d F ( x
...yes" , one says that the moment problem has a unique solution, or that the distribution function $F$ is M-determinate. Otherwise, the moment problem has a non-uniq
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A theorem characterizing the distribution of a random closed set in terms of the Choquet capacity functional [[#Refer
valued random element. Its distribution is described by the corresponding [[Probability measure|probability measure
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...encyclopediaofmath.org/legacyimages/e/e035/e035060/e0350603.png" /> is the distribution density of the random variable
is the density of the standard [[Normal distribution|normal distribution]], and
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be the number of cells in which, after distribution, there are exactly $ r $
and to study the asymptotic properties of their distribution as $ n , N \rightarrow \infty $.
7 KB (1,068 words) - 16:23, 4 March 2022
A numerical characteristic of the probability distribution of a random variable. In the most general setting, the mathematical expecta
with respect to the probability distribution $ {\mathsf P} _ {X} $
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[[Category:Distribution theory]]
of the given distribution series. If one restricts to the first few terms of the series (1), one obta
4 KB (578 words) - 11:31, 21 March 2022
...bution]]; [[Density of a probability distribution|Density of a probability distribution]]). Since $ \{ {\eta ( t ) } : {0 \leq t \leq 1 } \} $
frequently appear in [[Probability theory|probability theory]]. In particular, many limit distributions of the Bernoulli excursion $ \
4 KB (575 words) - 06:29, 30 May 2020
...n space of a random vector describing the concentration of its probability distribution around a certain prescribed vector in terms of the second-order moments. Le
called a dispersion ellipsoid of the probability distribution of $ X $
3 KB (375 words) - 16:43, 20 January 2022
''in probability theory''
...expectation of various functions of a random variable $X$ in terms of the distribution of this variable on the set of real numbers are of importance (cf. [[Mathem
7 KB (1,127 words) - 20:19, 27 January 2020
One of the simplest models in [[probability theory]]. A description of an urn model is as follows: Consider some vessel — an
...he Pólya distributions. The negative binomial distribution and the Poisson distribution arise as limit distributions from certain urn models.
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which automatically holds if the probability distribution of $ X $
is a [[Sufficient statistic|sufficient statistic]] for the distribution of $ X $,
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is the inverse function of the [[Normal distribution|normal distribution]] with parameters $ ( 0, 1) $.
individually, the asymptotic distribution of $ X $
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