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...hmetov. Analogues of Khintchine, Marcinkiewicz–Zygmund and Rosenthal inequalities for symmetric statistics. ''Scandinavian Journal of Statistics'', 26(4):621 [[Category:Statistical inequalities]] ...

| title=Some sharp inequalities for Martingale transforms The inequality has applications in statistical testing. ...

...arwal R P, Barnett N S, Cerone P and Dragomir S S (2005) "A survey on some inequalities for expectation and variance." ''Computers and mathematics with application == Comparisons to other inequalities == ...

...andom variables, with statistical applications", ''Journal of the American Statistical Association'', 88(243) 1026–1033</ref> ==Related inequalities== ...

...on entropy]].<ref>Tsallis, C. (2009) "Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years", ''Braz. J. Phys'', 39, 337–356</ref> The Tsallis distributions have been applied to problems in the fields of [[statistical mechanics]], [[geology]], [[anatomy]], [[astronomy]], [[economics]], [[fina ...

...bounds on the variance with applications|journal= Journal of Mathematical Inequalities|volume=4|issue=3|pages= 355–363 |doi=10.7153/jmi-04-32 |doi-access=free}}</ [[Category:Statistical inequalities]] ...

...ctions on a finite [[distributive lattice]]. It is a fundamental tool in [[statistical mechanics]] and [[Combinatorics#Probabilistic_combinatorics|probabilistic c ...t1=Rinott| first1=Yosef | last2=Saks | first2=Michael | title= Correlation inequalities and a conjecture for permanents | doi=10.1007/BF01202353 | year=1991| journ ...

...Sum of Independent Random Variables | journal = [[Journal of the American Statistical Association]] | volume = 57 | issue = 297 | pages = 33–45 | doi = 10.2307/2 ...-sUt1HZYC&pg=PA11}}</ref><ref name=BLM2013>{{cite book|title=Concentration inequalities, a nonasymptotic theory of independence | first1=Stephane | last1=Boucheron ...

It can be shown that these inequalities are the best possible and that further sharpening of the bounds requires th | title = Chebyshev inequalities for unimodal distributions ...

...Applications in Statistics and Matrix Theory |title=Analytic and Geometric Inequalities and Applications |pages=151–181 |doi=10.1007/978-94-011-4577-0_10 |isbn=978 ...quad \text{for } j = 1,\dots,n. </math><ref>{{cite book |title=Advances in Inequalities from Probability Theory and Statistics |first1=Neil S. |last1=Barnett |firs ...

...>{{citation | year=1992 | title = Convex functions, partial orderings, and statistical applications | author1=J. E. Pečarić | author2=Frank Proschan | author3=Yun ...}}</ref><ref>{{citation | author1=M.W. Alomari | title = Popoviciu’s type inequalities for h-MN-convex functions | volume=2021 | periodical=e-Journal of Analysis ...

...annals-of-mathematical-statistics/volume-31/issue-4/Multivariate-Chebyshev-Inequalities/10.1214/aoms/1177705673.full |journal=The Annals of Mathematical Statistics [[Category:Probabilistic inequalities]] ...

{{Short description|Class of confidence intervals around statistical functionals of a distribution}} ...ass of [[confidence interval]]s around [[V-statistic#Statistical functions|statistical functionals]] of a distribution. To calculate these confidence intervals, ...

...study of quantum field theories and related mathematical theories such as statistical mechanics. His early works developed the foundations of integration on infi ===Logarithmic Sobolev inequalities=== ...

{{Short description|Correlation inequality in statistical mechanics}} In [[statistical mechanics]], the '''Griffiths inequality''', sometimes also called '''Griff ...

...the [[Boole's inequality#Bonferroni inequalities|Boole–Bonferroni–Fréchet inequalities]], and to [[Copula (probability theory)#Fr.C3.A9chet.E2.80.93Hoeffding copu ...gical proposition]]s or [[Event (probability theory)|events]], the Fréchet inequalities are ...

In [[statistical mechanics]], an '''Ursell function''' or '''connected correlation function' *{{citation|mr=0378683 |last=Percus|first= J. K.|title= Correlation inequalities for Ising spin lattices|journal= Comm. Math. Phys. ...

...dent trials. Annals of Mathematical Statistics (27):713–721.</ref> In some statistical applications, the standard binomial variance estimator can be used even if ...ing#the testing process|null hypothesis]] is true for some tests and the [[statistical hypothesis testing#the testing process|alternative hypothesis]] is true for ...

...999-12-01|title=A new weak dependence condition and applications to moment inequalities|journal=Stochastic Processes and Their Applications|language=en|volume=84|i ...ators under a weak dependence condition|journal=Annals of the Institute of Statistical Mathematics|language=en|volume=42|issue=2|pages=305–329|doi=10.1007/bf00050 ...

====The first order inequalities==== ...fied from definitions or seen from the limit of the above Gibbs-Bogoliubov inequalities when ...