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Journal articles on the topic 'Central limit theorem'

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Published: 4 June 2021
Last updated: 29 July 2024

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1

Bianucci, Marco. "Operators central limit theorem." Chaos, Solitons & Fractals 148 (July 2021): 110961. http://dx.doi.org/10.1016/j.chaos.2021.110961.

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2

Bulinski, A. V. "Conditional Central Limit Theorem." Theory of Probability & Its Applications 61, no. 4 (January 2017): 613–31. http://dx.doi.org/10.1137/s0040585x97t98837x.

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3

de Jong, Robert M. "Central Limit Theorems for Dependent Heterogeneous Random Variables." Econometric Theory 13, no. 3 (June 1997): 353–67. http://dx.doi.org/10.1017/s0266466600005843.

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This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.
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4

Fazekas, István, and Alexey Chuprunov. "Almost sure limit theorems for random allocations." Studia Scientiarum Mathematicarum Hungarica 42, no. 2 (May 1, 2005): 173–94. http://dx.doi.org/10.1556/sscmath.42.2005.2.4.

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Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.
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5

Roginsky, Allen L. "A Central Limit Theorem for Cumulative Processes." Advances in Applied Probability 26, no. 1 (March 1994): 104–21. http://dx.doi.org/10.2307/1427582.

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A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.
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6

Roginsky, Allen L. "A Central Limit Theorem for Cumulative Processes." Advances in Applied Probability 26, no. 01 (March 1994): 104–21. http://dx.doi.org/10.1017/s0001867800026033.

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A central limit theorem for cumulative processes was first derived by Smith (1955). No remainder term was given. We use a different approach to obtain such a term here. The rate of convergence is the same as that in the central limit theorems for sequences of independent random variables.
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7

LIEBSCHER, VOLKMAR. "NOTE ON ENTANGLED ERGODIC THEOREMS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 02 (June 1999): 301–4. http://dx.doi.org/10.1142/s0219025799000175.

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We prove the entangled ergodic theorem, a notion recently proposed by Accardi, Hashimoto and Obata in connection with central limit theorems1 provided a multidimensional noncommutative analogue of the spectral theorem is valid. This shows at least the possible structure of limit states in such central limit theorems.
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8

Corcoran, Mimi. "Illustrating the Central Limit Theorem." Mathematics Teacher 109, no. 6 (February 2016): 456–62. http://dx.doi.org/10.5951/mathteacher.109.6.0456.

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9

Shashkin, A. P. "On Newman's Central Limit Theorem." Theory of Probability & Its Applications 50, no. 2 (January 2006): 330–37. http://dx.doi.org/10.1137/s0040585x97981731.

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10

Mitic, P. "The central limit theorem visualised." Teaching Mathematics and its Applications 15, no. 2 (June 1, 1996): 84–90. http://dx.doi.org/10.1093/teamat/15.2.84.

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11

Colwell, D. J., and J. R. Gillet. "Illustrating the Central Limit Theorem." Teaching Statistics 16, no. 2 (June 1994): 38. http://dx.doi.org/10.1111/j.1467-9639.1994.tb00683.x.

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12

Kerley, Lyndell M. "Comprehending the central limit theorem." ACM SIGCSE Bulletin 20, no. 2 (June 1988): 20–25. http://dx.doi.org/10.1145/45202.45208.

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13

Taylor, Marshall A. "Simulating the Central Limit Theorem." Stata Journal: Promoting communications on statistics and Stata 18, no. 2 (June 2018): 345–56. http://dx.doi.org/10.1177/1536867x1801800203.

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Understanding the central limit theorem is crucial for comprehending parametric inferential statistics. Despite this, undergraduate and graduate students alike often struggle with grasping how the theorem works and why researchers rely on its properties to draw inferences from a single unbiased random sample. In this article, I outline a new command, sdist, that can be used to simulate the central limit theorem by generating a matrix of randomly generated normal or nonnormal variables and comparing the true sampling distribution standard deviation with the standard error from the first randomly generated sample. The user also has the option of plotting the empirical sampling distribution of sample means, the first random variable distribution, and a stacked visualization of the two distributions.
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14

Wu, Xinxing, and Guanrong Chen. "Central limit theorem and chaoticity." Statistics & Probability Letters 92 (September 2014): 137–42. http://dx.doi.org/10.1016/j.spl.2014.05.017.

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15

Weber, Michel. "A weighted central limit theorem." Statistics & Probability Letters 76, no. 14 (August 2006): 1482–87. http://dx.doi.org/10.1016/j.spl.2006.03.007.

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16

Blacher, René. "Central Limit Theorem by moments." Statistics & Probability Letters 77, no. 17 (November 2007): 1647–51. http://dx.doi.org/10.1016/j.spl.2007.04.003.

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17

Eliazar, Iddo, and Joseph Klafter. "A Randomized Central Limit Theorem." Chemical Physics 370, no. 1-3 (May 2010): 290–93. http://dx.doi.org/10.1016/j.chemphys.2009.11.010.

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18

Hu, Feng, and Defei Zhang. "Central limit theorem for capacities." Comptes Rendus Mathematique 348, no. 19-20 (October 2010): 1111–14. http://dx.doi.org/10.1016/j.crma.2010.07.026.

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19

Johnson, David E. "Demonstrating the Central Limit Theorem." Teaching of Psychology 13, no. 3 (October 1986): 155–56. http://dx.doi.org/10.1207/s15328023top1303_18.

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Explaining abstract, theoretical distributions to beginning students is sometimes difficult. This article describes a demonstration that helps to make the central limit theorem for generating sampling distributions concrete and understandable.
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20

Ganicheva, Antonina. "ESTIMATION OF THE NUMBER OF SUMMANDS OF THE CENTRAL LIMIT THEOREM." Applied Mathematics and Control Sciences, no. 4 (December 15, 2020): 7–19. http://dx.doi.org/10.15593/2499-9873/2020.4.01.

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The problem of estimating the number of summands of random variables for a total normal distribution law or a sample average with a normal distribution is investigated. The Central limit theorem allows us to solve many complex applied problems using the developed mathematical apparatus of the normal probability distribution. Otherwise, we would have to operate with convolutions of distributions that are explicitly calculated in rare cases. The purpose of this paper is to theoretically estimate the number of terms of the Central limit theorem necessary for the sum or sample average to have a normal probability distribution law. The article proves two theorems and two consequences of them. The method of characteristic functions is used to prove theorems. The first theorem States the conditions under which the average sample of independent terms will have a normal distribution law with a given accuracy. The corollary of the first theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 1. The second theorem defines the normal distribution conditions for the average sample of independent random variables whose mathematical expectations fall in the same interval, and whose variances also fall in the same interval. The corollary of the second theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 2. According to the formula relations proved in theorem 1, a table of the required number of terms in the Central limit theorem is calculated to ensure the specified accuracy of approximation of the distribution of the values of the sample average to the normal distribution law. A graph of this dependence is constructed. The dependence is well approximated by a polynomial of the sixth degree. The relations and proved theorems obtained in the article are simple, from the point of view of calculations, and allow controlling the testing process for evaluating students ' knowledge. They make it possible to determine the number of experts when making collective decisions in the economy and organizational management systems, to conduct optimal selective quality control of products, to carry out the necessary number of observations and reasonable diagnostics in medicine.
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21

Belovas, Igoris. "Central and Local Limit Theorems for Numbers of the Tribonacci Triangle." Mathematics 9, no. 8 (April 16, 2021): 880. http://dx.doi.org/10.3390/math9080880.

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In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.
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22

Jiang, Yuanying, and Qunying Wu. "The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/656257.

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In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables:limn→∞(1/logn)∑k=1n(I(ak≤Sk<bk)/k)P(ak≤Sk<bk)=1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central limit theorems from the i.i.d. case to the stationary negatively associated sequences.
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23

RÉVEILLAC, ANTHONY, MICHAEL STAUCH, and CIPRIAN A. TUDOR. "HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET." Stochastics and Dynamics 12, no. 03 (May 16, 2012): 1150021. http://dx.doi.org/10.1142/s0219493711500213.

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We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet Wα, βwith Hurst parameter (α, β) ∈ (0, 1)2. When [Formula: see text] or [Formula: see text] a central limit theorem holds for the renormalized Hermite variations of order q ≥ 2, while for [Formula: see text] we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time (1, 1).
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24

Akritas, Michael G. "The Central Limit Theorem under Censoring." Bernoulli 6, no. 6 (December 2000): 1109. http://dx.doi.org/10.2307/3318473.

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25

Colwell, D. J., J. R. Gillett, and P. L. B. Worthington. "71.41 Illustrating the Central Limit Theorem." Mathematical Gazette 71, no. 458 (December 1987): 300. http://dx.doi.org/10.2307/3617054.

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26

Ahn, Young-Ho. "CENTRAL LIMIT THEOREM ON CHEBYSHEV POLYNOMIALS." Pure and Applied Mathematics 21, no. 4 (November 30, 2014): 271–79. http://dx.doi.org/10.7468/jksmeb.2014.21.4.271.

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27

CALLENDER, JOHN, and ROGER JACKSON. "The Central Limit Theorem—a Demonstration." Teaching Mathematics and its Applications 8, no. 1 (1989): 17–22. http://dx.doi.org/10.1093/teamat/8.1.17.

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28

Vignat, C., and A. Plastino. "Central limit theorem and deformed exponentials." Journal of Physics A: Mathematical and Theoretical 40, no. 45 (October 23, 2007): F969—F978. http://dx.doi.org/10.1088/1751-8113/40/45/f02.

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29

Fante, R. L. "Central limit theorem: Use with caution." IEEE Transactions on Aerospace and Electronic Systems 37, no. 2 (April 2001): 739–40. http://dx.doi.org/10.1109/7.937486.

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30

Peligrad, Magda, and Sergey Utev. "Central limit theorem for linear processes." Annals of Probability 25, no. 1 (January 1997): 443–56. http://dx.doi.org/10.1214/aop/1024404295.

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31

Ledrappier, Francois. "Central Limit Theorem in Negative Curvature." Annals of Probability 23, no. 3 (July 1995): 1219–33. http://dx.doi.org/10.1214/aop/1176988181.

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32

Cam, L. Le. "The Central Limit Theorem Around 1935." Statistical Science 1, no. 1 (February 1986): 78–91. http://dx.doi.org/10.1214/ss/1177013818.

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33

Benoist, Y., and J.-F. Quint. "Central limit theorem on hyperbolic groups." Izvestiya: Mathematics 80, no. 1 (February 28, 2016): 3–23. http://dx.doi.org/10.1070/im8306.

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34

Kuperberg, Greg. "A tracial quantum central limit theorem." Transactions of the American Mathematical Society 357, no. 2 (December 15, 2003): 459–71. http://dx.doi.org/10.1090/s0002-9947-03-03449-4.

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35

Krylov, N. V. "On Shige Peng’s central limit theorem." Stochastic Processes and their Applications 130, no. 3 (March 2020): 1426–34. http://dx.doi.org/10.1016/j.spa.2019.05.005.

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36

Brosamler, Gunnar A. "An almost everywhere central limit theorem." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 3 (November 1988): 561–74. http://dx.doi.org/10.1017/s0305004100065750.

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The purpose of this paper is the proof of an almost everywhere version of the classical central limit theorem (CLT). As is well known, the latter states that for IID random variables Y1, Y2, … on a probability space (Ω, , P) with we have weak convergence of the distributions of to the standard normal distribution on ℝ. We recall that weak convergence of finite measures μn on a metric space S to a finite measure μ on S is defined to mean thatfor all bounded, continuous real functions on S. Equivalently, one may require the validity of (1·1) only for bounded, uniformly continuous real functions, or even for all bounded measurable real functions which are μ-a.e. continuous.
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37

Barron, Andrew R. "Entropy and the Central Limit Theorem." Annals of Probability 14, no. 1 (January 1986): 336–42. http://dx.doi.org/10.1214/aop/1176992632.

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38

Matz, David C., and Emily L. Hause. "“Dealing” With the Central Limit Theorem." Teaching of Psychology 35, no. 3 (July 22, 2008): 198–200. http://dx.doi.org/10.1080/00986280802186201.

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39

Chareka, Patrick. "The central limit theorem for capacities." Statistics & Probability Letters 79, no. 12 (June 2009): 1456–62. http://dx.doi.org/10.1016/j.spl.2009.03.015.

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40

Niu, Yingxuan, and Yi Wang. "The central limit theorem and ergodicity." Statistics & Probability Letters 80, no. 15-16 (August 2010): 1180–84. http://dx.doi.org/10.1016/j.spl.2010.03.014.

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41

B�ez-Duarte, L. "Central limit theorem for complex measures." Journal of Theoretical Probability 6, no. 1 (January 1993): 33–56. http://dx.doi.org/10.1007/bf01046767.

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42

Speicher, Roland. "A non-commutative central limit theorem." Mathematische Zeitschrift 209, no. 1 (January 1992): 55–66. http://dx.doi.org/10.1007/bf02570820.

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43

Bobkov, Sergey G. "Central Limit Theorem and Diophantine Approximations." Journal of Theoretical Probability 31, no. 4 (June 30, 2017): 2390–411. http://dx.doi.org/10.1007/s10959-017-0770-4.

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44

Rhee, WanSoo T. "Central limit theorem and increment conditions." Statistics & Probability Letters 4, no. 4 (June 1986): 191–95. http://dx.doi.org/10.1016/0167-7152(86)90065-9.

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45

Griniv, O. O. "Central limit theorem for Burgers equation." Theoretical and Mathematical Physics 88, no. 1 (July 1991): 678–82. http://dx.doi.org/10.1007/bf01016331.

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46

Gonçalves, Felipe. "A central limit theorem for operators." Journal of Functional Analysis 271, no. 6 (September 2016): 1585–603. http://dx.doi.org/10.1016/j.jfa.2016.06.008.

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47

Alberty, J. M., and A. Białas. "Intermittency and the central limit theorem." Zeitschrift für Physik C Particles and Fields 50, no. 2 (June 1991): 315–20. http://dx.doi.org/10.1007/bf01474084.

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48

Matz, David C., and Emily L. Hause. "“Dealing” with the Central Limit Theorem." Teaching of Psychology 35, no. 3 (July 2008): 198–200. http://dx.doi.org/10.1177/009862830803500308.

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49

Benoist, Yves, and Jean-François Quint. "Central limit theorem for linear groups." Annals of Probability 44, no. 2 (March 2016): 1308–40. http://dx.doi.org/10.1214/15-aop1002.

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50

Barbour, Andrew, and Svante Janson. "A Functional Combinatorial Central Limit Theorem." Electronic Journal of Probability 14 (2009): 2352–70. http://dx.doi.org/10.1214/ejp.v14-709.

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