converges in distribution to $ f ( W ) $,
is a Wiener random function. Thus, the limiting distribution for the $ f ( Y _ {n} ) $
3 KB (432 words) - 19:45, 16 January 2024
...sen independently of the others and in accordance with a given probability distribution. Sometimes a random coding is defined in such a way that every realization
...><TD valign="top">[3]</TD> <TD valign="top"> R. Gallagher, "Information theory and reliable communication" , Wiley (1968)</TD></TR></table>
2 KB (258 words) - 17:04, 7 February 2011
have a given continuous distribution function $ F (x) $.
is the [[Empirical distribution|empirical distribution]] function constructed from the sample $ X _{1} \dots X _{n} $
4 KB (572 words) - 11:08, 26 March 2023
...Goodness-of-fit test|Goodness-of-fit test]]) one wants to test whether the distribution function of a [[Random variable|random variable]] $ X $
...e simplest case this set consists of one completely specified (continuous) distribution function $ F _ {0} $,
5 KB (709 words) - 06:49, 26 March 2023
...s distribution in Gauss' theory of errors (cf. [[Errors, theory of|Errors, theory of]]). The densities
2 KB (315 words) - 19:41, 5 June 2020
...sion of the [[Central limit theorem|Central Limit Theorem]] of probability theory: If $ S_{n} $ denotes the number of “successes” in $ n $ [[Bernoulli tr
is the cumulative distribution function of the standard normal law.
5 KB (692 words) - 19:33, 7 July 2016
...in an arcsine distribution or a generalized [[Arcsine distribution|arcsine distribution]]. The following feature of a Brownian motion $ \{ {\xi _ {t} } : {t \geq
will then have the arcsine distribution:
4 KB (576 words) - 18:48, 5 April 2020
that is, the [[Joint distribution|joint distribution]] of $ X _ {1} \dots X _ {k} $
To test the hypothesis of no relationship, the sampling distribution of $ r _ {1 \cdot ( 2 \dots k) } $
5 KB (666 words) - 08:02, 6 June 2020
...p=0.25$, has the name inter-quartile distance, and in the case of a normal distribution it is equal to $1.349\sigma$ (where $\sigma$ is the natural measure of disp
...ign="top">[1]</TD> <TD valign="top"> G.U. Yale, "An introduction to the theory of statistics" , Griffin (1916)</TD></TR></table>
1 KB (190 words) - 21:50, 9 November 2014
...oper distributions is a normal distribution, then each of them is a normal distribution; and 2) if $\phi_1(t)$ and $\phi_2(t)$ are characteristic functions and if
...mplies closeness of the distribution of each of the summands to the normal distribution; qualitative estimates of the stability are known.
4 KB (647 words) - 19:21, 24 March 2023
...e, instead of the term "non-parametric test" one speaks frequently of a "distribution-free test" . The [[Kolmogorov test]] is a classic example of a non-parametr
....Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)</TD></TR>
2 KB (247 words) - 09:06, 10 April 2023
...(for a classical system — towards the local [[Maxwell distribution|Maxwell distribution]]), i.e. being always larger than the times of formation of the local hydro
...ction, corresponding to the case of a small deviation from a local Maxwell distribution, is then substituted into these equations. In the zero-th approximation thi
4 KB (525 words) - 20:13, 12 October 2014
...andard one) in terms of the corresponding quantiles of the standard normal distribution, in powers of a small parameter. It was studied by E.A. Cornish and R.A. Fi
is a distribution function depending on $ t $
4 KB (608 words) - 16:41, 15 January 2021
A concept in value-distribution theory. Let $f(z)$ be a meromorphic function in the whole $z$-plane and let $n(r,a
...$f$ to $a$ on $|z|=r$ (cf. [[Value-distribution theory|Value-distribution theory]]). For the majority of values $a$ the quantities $N(r,a,f)$ and $T(r,f)$ a
3 KB (495 words) - 09:04, 26 November 2023
...g to a given probability distribution. In [[Probability theory|probability theory]], attention centres on numerical (that is, scalar) random functions $ X
...-dimensional (vector) random variable characterized by a multi-dimensional distribution function. When $ T $
7 KB (1,062 words) - 08:09, 6 June 2020
Poisson's theorem is a limit theorem in probability theory which is a particular case of the [[Law of large numbers|law of large numbe
...distribution|binomial distribution]] to the [[Poisson distribution|Poisson distribution]]: If $ P _ {n} ( m) $
4 KB (651 words) - 08:06, 6 June 2020
''probability distribution, probability''
(the [[Poisson distribution|Poisson distribution]]);
3 KB (421 words) - 19:48, 8 January 2021
...undaries and knowing the initial step distribution at time $t_0$, the step distribution at $t_0+\Delta t$ is calculated using the mass, momentum and energy balance
...extended to problems of hydrodynamics with heat conduction, to elasticity theory, etc. Owing to an obvious physical interpretation and universality, and sin
3 KB (431 words) - 10:52, 16 April 2014
''in probability theory''
...f the densities of a sequence of distributions to the density of the limit distribution (if the given densities exist), or a classical version of local limit theor
6 KB (856 words) - 15:13, 18 March 2022
...notions of the concept of convergence, of which the most important for the theory of statistical estimation are convergence in probability and convergence wi
be independent random variables with the same normal distribution $ N ( a, \sigma ^ {2} ) $.
4 KB (501 words) - 17:46, 4 June 2020