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...rational partition function'''<ref name="McQuarrie">Donald A. McQuarrie, ''Statistical Mechanics'', Harper & Row, 1973</ref> traditionally refers to the component == Approximations == ...

...pproximations of a step function|thumb|Several progressively more accurate approximations of the [[step function]].]] ....1016/S0167-7012(00)00201-3|pmid=11084225|s2cid=18267806 }}</ref> Function approximations are used where theoretical models are unavailable or hard to compute.<ref n ...

...n providing approximations to the [[cumulative distribution function]]s of statistical [[estimator]]s. ...the asymptotic distribution is ''F'' then, for large ''n'', the following approximations hold ...

* <math>X_1, X_2, X_3, \ldots </math> are [[statistical independence|independent]] [[random variable]]s, each with a [[Bernoulli di ...| last1 = Steele | first1 = J. M.| title = Le Cam's Inequality and Poisson Approximations | jstor = 2325124 | journal = The American Mathematical Monthly | volume = ...

The result can be used to perform approximate [[statistical inference]] tests. The simplest application of this equation is in perform | title = Applied Linear Statistical Models ...

|title=Introductory Statistical Mechanics ==Other approximations of thermal radiation== ...

*[[Statistical dispersion|Measures of dispersion *[[Statistical graphics]] ...

In a [[statistical classification|statistical-classification]] problem with two classes, a '''decision boundary''' or ''' ...y| first2 = Susan A.| title = Rejoinder| journal = Journal of the American Statistical Association| accessdate = 2022-11-28| date = 2011| doi = 10.1198/jasa.2011. ...

In [[statistical physics]], the '''Bogoliubov–Born–Green–Kirkwood–Yvon''' ('''BBGKY''') '''h ...ation]]s and the first order corrections to the Boltzmann equations. Other approximations, such as the assumption that the density probability function depends only ...

...[model selection]] problems where the [[posterior distribution]]s of the [[statistical model|model]]s have been obtained by [[Markov chain Monte Carlo]] (MCMC) si ...samples of <math> \theta</math>. Then the DIC follows directly from these approximations. Claeskens and Hjort (2008, Ch. 3.5) show that the DIC is [[asymptotic dist ...

...tatistical test]] such that if the [[null hypothesis]] is true, then all [[Statistical assumption|assumptions]] made during the derivation of the distribution of Hence, when a result of statistical analysis is termed an “exact test” or specifies an “exact [[p-value]]”, thi ...

If ''X'' is a [[Multivariate random variable|random vector]], the approximations for the mean and variance of <math>f(X)</math> are given by<ref>{{Cite jour [[Category:Statistical approximations]] ...

When [[classification]] is performed by a computer, statistical methods are normally used to develop the algorithm. ...tion is [[probabilistic classification]]. Algorithms of this nature use [[statistical inference]] to find the best class for a given instance. Unlike other algo ...

...heory)|filtration]]. It may be thought of as the evolving sequence of best approximations to the random variable based on information accumulated up to a certain tim When analyzing sums, [[random walk]]s, or other additive functions of [[Statistical independence|independent random variables]], one can often apply the [[cent ...

* a measure of [[statistical dispersion]] like the [[standard deviation|standard mean absolute deviation ...e than one variable is measured, a measure of [[correlation and dependence|statistical dependence]] such as a [[Pearson product-moment correlation coefficient|cor ...

{{Short description|Test of statistical significance}} '''Binomial test''' is an [[exact test]] of the [[statistical significance]] of deviations from a theoretically expected distribution of ...

...trary function, so importance sampling algorithms aim to produce efficient approximations to the desired distribution. [[Category:Statistical algorithms]] ...

...mistry|quantum theory]], [[mathematical physics]], [[statistical mechanics|statistical]] and [[classical mechanics|classical]] mechanics, [[chemical kinetics]], a ...in chemical phenomena at the microscopic level, such as quantum mechanics, statistical mechanics, and molecular dynamics. Meanwhile, physical chemistry uses a bro ...

...as [[Khinchin's constant]]. He also published several important works on [[statistical physics]], where he used the methods of probability theory, and on [[inform *[[Khinchin's theorem on Diophantine approximations]] ...

...t1=Lehmann |first1=Erich L. |last2=Romano |first2=Joseph P. |title=Testing statistical hypotheses |date=2022 |publisher=Springer |location=Cham |isbn=978-3-030-70 ...st4=Koike |first4=Yuta |title=Improved central limit theorem and bootstrap approximations in high dimensions |journal=Annals of Statistics |date=October 2022 |volume ...