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Journal articles on the topic 'Limit distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Meyrath, Thierry, and Markus Nieß. "Universal distribution of limit points." Acta Mathematica Hungarica 133, no. 3 (2011): 288–303. http://dx.doi.org/10.1007/s10474-011-0114-2.

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2

Taylor, Marshall A. "Simulating the Central Limit Theorem." Stata Journal: Promoting communications on statistics and Stata 18, no. 2 (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 randoml

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3

Chen, Xiaohong, and Halbert White. "CENTRAL LIMIT AND FUNCTIONAL CENTRAL LIMIT THEOREMS FOR HILBERT-VALUED DEPENDENT HETEROGENEOUS ARRAYS WITH APPLICATIONS." Econometric Theory 14, no. 2 (1998): 260–84. http://dx.doi.org/10.1017/s0266466698142056.

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We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent observations: (1) A new CLT for any plug-in estimator of a cumulative distribution function (c.d.f.) (e.g., an empirical c.d.f.,

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4

Boyarinov, R. N. "Rate of convergence to limit distribution." Moscow University Mathematics Bulletin 66, no. 2 (2011): 70–76. http://dx.doi.org/10.3103/s0027132211020033.

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5

Shimura, Takaaki. "Limit distribution of a roundoff error." Statistics & Probability Letters 82, no. 4 (2012): 713–19. http://dx.doi.org/10.1016/j.spl.2011.12.021.

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6

Luna, E. G. S., and A. A. Natale. "Limit on the pion distribution amplitude." Journal of Physics G: Nuclear and Particle Physics 42, no. 1 (2014): 015003. http://dx.doi.org/10.1088/0954-3899/42/1/015003.

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7

Primack, Richard B., and S. L. Miao. "Dispersal Can Limit Local Plant Distribution." Conservation Biology 6, no. 4 (1992): 513–19. http://dx.doi.org/10.1046/j.1523-1739.1992.06040513.x.

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8

Timashev, Aleksandr N. "Limit theorems for some classes of power series type distributions." Discrete Mathematics and Applications 30, no. 1 (2020): 69–78. http://dx.doi.org/10.1515/dma-2020-0007.

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AbstractSeveral classes of distributions of power series type with finite and infinite radii of convergence are considered. For such distributions local limit theorems are obtained as the parameter of distribution tends to the right end of the interval of convergence. For the case when the convergence radius equals to 1, we prove an integral limit theorem on the convergence of distributions of random variables (1 − x)ξxas x → 1− to the gamma-distribution (ξx is a random variable with corresponding distribution of the power series type). The proofs are based on the steepest descent method.

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9

Tomisaki, Matsuyo, and Makoto Yamazato. "Limit theorems for hitting times of 1-dimensional generalized diffusions." Nagoya Mathematical Journal 152 (December 1998): 1–37. http://dx.doi.org/10.1017/s0027763000006784.

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Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the

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10

Khokhlov, Yury, Victor Korolev, and Alexander Zeifman. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems." Mathematics 8, no. 5 (2020): 749. http://dx.doi.org/10.3390/math8050749.

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In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these distributions are discussed. The main focus is on the representations of the corresponding random vectors as products of independent random variables and vectors. In these products, relations are traced of the distributions of the involved terms with popular probability distributions. As examples of distributions of the class of scale mixtures of multiva

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11

Macutek, Jan, and Jan Macutek. "A limit property of the geometric distribution." Teoriya Veroyatnostei i ee Primeneniya 50, no. 2 (2005): 404–8. http://dx.doi.org/10.4213/tvp119.

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12

Devroye, Luc, James Fill, and Ralph Neininger. "Perfect Simulation from the Quicksort Limit Distribution." Electronic Communications in Probability 5 (2000): 95–99. http://dx.doi.org/10.1214/ecp.v5-1024.

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13

de Haan, L., and Sidney I. Resnick. "Estimating the limit distribution of multivariate extremes." Communications in Statistics. Stochastic Models 9, no. 2 (1993): 275–309. http://dx.doi.org/10.1080/15326349308807267.

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14

Burakovsky, L., and L. P. Horwitz. "Galilean limit of equilibrium relativistic mass distribution." Journal of Physics A: Mathematical and General 27, no. 8 (1994): 2623–31. http://dx.doi.org/10.1088/0305-4470/27/8/003.

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15

Cabello, Adán. "Quantum Key Distribution in the Holevo Limit." Physical Review Letters 85, no. 26 (2000): 5635–38. http://dx.doi.org/10.1103/physrevlett.85.5635.

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16

Yashunsky, Alexey Dmitrievich. "On limit points of Bernoulli distribution algebras." Keldysh Institute Preprints, no. 270 (2018): 1–16. http://dx.doi.org/10.20948/prepr-2018-270.

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17

Macutek, J. "A Limit Property of the Geometric Distribution." Theory of Probability & Its Applications 50, no. 2 (2006): 316–19. http://dx.doi.org/10.1137/s0040585x97981767.

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18

Strömbergsson, Andreas. "On the limit distribution of Frobenius numbers." Acta Arithmetica 152, no. 1 (2012): 81–107. http://dx.doi.org/10.4064/aa152-1-7.

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19

Li, Han. "Effective limit distribution of the Frobenius numbers." Compositio Mathematica 151, no. 5 (2014): 898–916. http://dx.doi.org/10.1112/s0010437x14007866.

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The Frobenius number$F(\boldsymbol{a})$of a lattice point$\boldsymbol{a}$in$\mathbb{R}^{d}$with positive coprime coordinates, is the largest integer which cannotbe expressed as a non-negative integer linear combination of the coordinates of$\boldsymbol{a}$. Marklof in [The asymptotic distribution of Frobenius numbers, Invent. Math.181(2010), 179–207] proved the existence of the limit distribution of the Frobenius numbers, when$\boldsymbol{a}$is taken to be random in an enlarging domain in$\mathbb{R}^{d}$. We will show that if the domain has piecewise smooth boundary, the error term for the con

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20

Broniatowski, Michel, and Virgile Caron. "Long runs under a conditional limit distribution." Annals of Applied Probability 24, no. 6 (2014): 2246–96. http://dx.doi.org/10.1214/13-aap975.

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21

Hudson, William N., Howard G. Tucker, and Jerry A. Veeh. "Limit theorems for the multivariate binomial distribution." Journal of Multivariate Analysis 18, no. 1 (1986): 32–45. http://dx.doi.org/10.1016/0047-259x(86)90056-4.

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22

Banek, Tadeusz, Patrycja Jędrzejewska, and August M. Zapała. "Limit Distribution of the Banach Random Walk." Journal of Theoretical Probability 32, no. 1 (2018): 47–63. http://dx.doi.org/10.1007/s10959-018-0858-5.

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23

Pfanzagl, J. "Asymptotic bounds for estimators without limit distribution." Annals of the Institute of Statistical Mathematics 55, no. 1 (2003): 95–110. http://dx.doi.org/10.1007/bf02530487.

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24

Šliogere, Jūratė, and Vydas Čekanavičius. "Two limit theorems for Markov binomial distribution." Lithuanian Mathematical Journal 55, no. 3 (2015): 451–63. http://dx.doi.org/10.1007/s10986-015-9291-y.

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25

Ostrovsky, Dmitry. "Mellin Transform of the Limit Lognormal Distribution." Communications in Mathematical Physics 288, no. 1 (2009): 287–310. http://dx.doi.org/10.1007/s00220-009-0771-y.

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26

Savelov, Maxim P. "Limit distributions of the Pearson statistics for nonhomogeneous polynomial scheme." Discrete Mathematics and Applications 29, no. 4 (2019): 233–39. http://dx.doi.org/10.1515/dma-2019-0021.

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Abstract For a nonhomogeneous polynomial scheme, conditions are found under which the Pearson statistic distributions converge to the distribution of nonnegative quadratic form of independent random variables with the standard normal distribution.

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27

Bar-Lev, Shaul K., Ernst Schulte-Geers, and Wolfgang Stadje. "Conditional Limit Theorems for the Terms of a Random Walk Revisited." Journal of Applied Probability 50, no. 3 (2013): 871–82. http://dx.doi.org/10.1239/jap/1378401242.

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In this paper we derive limit theorems for the conditional distribution ofX1givenSn=snasn→ ∞, where theXiare independent and identically distributed (i.i.d.) random variables,Sn=X1+··· +Xn, andsn/nconverges orsn≡sis constant. We obtain convergence in total variation of PX1∣Sn/n=sto a distribution associated to that ofX1and of PnX1∣Sn=sto a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.

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28

Socoll, Sanda N., and A. D. Barbour. "Local Limit Approximations for Markov Population Processes." Journal of Applied Probability 46, no. 03 (2009): 690–708. http://dx.doi.org/10.1017/s0021900200005829.

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In this paper we are concerned with the equilibrium distribution ∏ n of the nth element in a sequence of continuous-time density-dependent Markov processes on the integers. Under a (2+α)th moment condition on the jump distributions, we establish a bound of order O(n -(α+1)/2√logn) on the difference between the point probabilities of ∏ n and those of a translated Poisson distribution with the same variance. Except for the factor √logn, the result is as good as could be obtained in the simpler setting of sums of independent, integer-valued random variables. Our arguments are based on the Stein-C

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29

Socoll, Sanda N., and A. D. Barbour. "Local Limit Approximations for Markov Population Processes." Journal of Applied Probability 46, no. 3 (2009): 690–708. http://dx.doi.org/10.1239/jap/1253279846.

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In this paper we are concerned with the equilibrium distribution ∏n of the nth element in a sequence of continuous-time density-dependent Markov processes on the integers. Under a (2+α)th moment condition on the jump distributions, we establish a bound of order O(n-(α+1)/2√logn) on the difference between the point probabilities of ∏n and those of a translated Poisson distribution with the same variance. Except for the factor √logn, the result is as good as could be obtained in the simpler setting of sums of independent, integer-valued random variables. Our arguments are based on the Stein-Chen

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30

Gao, Mingchu. "Two-faced families of non-commutative random variables having bi-free infinitely divisible distributions." International Journal of Mathematics 27, no. 04 (2016): 1650037. http://dx.doi.org/10.1142/s0129167x16500373.

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We study two-faced families of non-commutative random variables having bi-free (additive) infinitely divisible distributions. We prove a limit theorem of the sums of bi-free two-faced families of random variables within a triangular array. As a corollary of our limit theorem, we get Voiculescu’s bi-free central limit theorem. Using the full Fock space operator model, we show that a two-faced pair of random variables has a bi-free (additive) infinitely divisible distribution if and only if its distribution is the limit distribution in our limit theorem. Finally, we characterize the bi-free (add

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31

Keightley, Peter D. "Inference of Genome-Wide Mutation Rates and Distributions of Mutation Effects for Fitness Traits: A Simulation Study." Genetics 150, no. 3 (1998): 1283–93. http://dx.doi.org/10.1093/genetics/150.3.1283.

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Abstract The properties and limitations of maximum likelihood (ML) inference of genome-wide mutation rates (U) and parameters of distributions of mutation effects are investigated. Mutation parameters are estimated from simulated experiments in which mutations randomly accumulate in inbred lines. ML produces more accurate estimates than the procedure of Bateman and Mukai and is more robust if the data do not conform to the model assumed. Unbiased ML estimates of the mutation effects distribution parameters can be obtained if a value for U can be assumed, but if U is estimated simultaneously wi

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32

Minami, Mihoko. "Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions." Journal of Statistical Planning and Inference 137, no. 11 (2007): 3626–33. http://dx.doi.org/10.1016/j.jspi.2007.03.038.

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33

Klee, G. G. "Tolerance limits for short-term analytical bias and analytical imprecision derived from clinical assay specificity." Clinical Chemistry 39, no. 7 (1993): 1514–18. http://dx.doi.org/10.1093/clinchem/39.7.1514.

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Abstract I propose a method for defining tolerance limits for assay bias and assay imprecision, based on the effects of these tolerance limits on the clinical specificity of the assay. An analytical "error budget" is defined as the squared sums of the imprecision and bias errors. The maximum limit for this error budget is set at a value corresponding to a 50% increase in the false-positive rate for classifying healthy subjects. For gaussian distributions with +/- 2 SD used as decision limits, this error budget equates to 0.45 SD of combined within-person and between-person biological variation

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34

Bar-Lev, Shaul K., Ernst Schulte-Geers, and Wolfgang Stadje. "Conditional Limit Theorems for the Terms of a Random Walk Revisited." Journal of Applied Probability 50, no. 03 (2013): 871–82. http://dx.doi.org/10.1017/s0021900200009906.

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In this paper we derive limit theorems for the conditional distribution of X 1 given S n =s n as n→ ∞, where the X i are independent and identically distributed (i.i.d.) random variables, S n =X 1+··· +X n , and s n /n converges or s n ≡ s is constant. We obtain convergence in total variation of P X 1∣ S n /n=s to a distribution associated to that of X 1 and of P nX 1∣ S n =s to a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.

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35

MARKLOF, JENS. "The $\bm{n}$-point correlations between values of a linear form." Ergodic Theory and Dynamical Systems 20, no. 4 (2000): 1127–72. http://dx.doi.org/10.1017/s0143385700000626.

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We show that the $n$-point correlation function for the fractional parts of a random linear form in $m$ variables has a limit distribution with power-like tail. The existence of the limit distribution follows from the mixing property of flows on ${\rm SL}(m+1,{\Bbb R})/{\rm SL}(m+1,{\Bbb Z})$. Moreover, we prove similar limit theorems (i) for the probability to find the fractional part of a random linear form close to zero and (ii) also for related trigonometric sums. For large $m$, all of the above limit distributions approach the classical distributions for independent uniformly distributed

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36

ZHANG, TONGHUA, HONG ZANG, and MOSE O. TADE. "BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP." International Journal of Bifurcation and Chaos 23, no. 04 (2013): 1350067. http://dx.doi.org/10.1142/s0218127413500673.

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This paper is concerned with the distribution and number of limit cycles for a cubic Hamiltonian system under cubic perturbation. The fact that there exist seven limit cycles is proved. The different distributions of limit cycles are given by using the methods of bifurcation theory and qualitative analysis, and the distributions of seven limit cycles are newly established.

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37

Molchanov, Ilya S. "Limit theorems for convex hulls of random sets." Advances in Applied Probability 25, no. 2 (1993): 395–414. http://dx.doi.org/10.2307/1427659.

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Let , be i.i.d. random closed sets in . Limit theorems for their normalized convex hulls conv () are proved. The limiting distributions correspond to C-stable random sets. The random closed set A is called C-stable if, for any , the sets anA and conv ( coincide in distribution for certain positive an, compact Kn, and independent copies A1, …, An of A. The distributions of C-stable sets are characterized via corresponding containment functionals.

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38

Konzou, Essomanda. "Stein's method in two limit theorems involving the generalized inverse Gaussian distribution." Afrika Statistika 16, no. 1 (2021): 2561–86. http://dx.doi.org/10.16929/as/2021.2561.174.

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The generalized hyperbolic (GH) distribution converges in law to the generalized inverse Gaussian (GIG) distribution under certain conditions on the parameters. When the edges of an infinite rooted tree are equipped with independent resistances that are inverse Gaussian or reciprocal inverse Gaussian distributions, the total resistance converges almost surely to some random variable which follows the reciprocal inverse Gaussian (RIG) distribution. In this paper we provide explicit upper bounds for the distributional distance between GH (resp. infinite tree) distribution and their limiting GIG

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39

Molchanov, Ilya S. "Limit theorems for convex hulls of random sets." Advances in Applied Probability 25, no. 02 (1993): 395–414. http://dx.doi.org/10.1017/s0001867800025416.

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Let , be i.i.d. random closed sets in . Limit theorems for their normalized convex hulls conv () are proved. The limiting distributions correspond to C-stable random sets. The random closed set A is called C-stable if, for any , the sets anA and conv ( coincide in distribution for certain positive an, compact Kn , and independent copies A 1, …, An of A. The distributions of C-stable sets are characterized via corresponding containment functionals.

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40

Machida, Takuya. "A localized quantum walk with a gap in distribution." Quantum Information and Computation 16, no. 5&6 (2016): 516–29. http://dx.doi.org/10.26421/qic16.5-6-7.

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Quantum walks behave differently from what we expect and their probability distributions have unique structures. They have localization, singularities, a gap, and so on. Those features have been discovered from the view point of mathematics and reported as limit theorems. In this paper we focus on a time-dependent three-state quantum walk on the line and demonstrate a limit distribution. Three coin states at each position are iteratively updated by a coin-flip operator and a position-shift operator. As the result of the evolution, we end up to observe both localization and a gap in the limit d

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41

Liao, Xin, Zuoxiang Peng, and Saralees Nadarajah. "Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution." Communications in Statistics - Theory and Methods 43, no. 24 (2014): 5276–89. http://dx.doi.org/10.1080/03610926.2012.730168.

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42

Wang, Yazhen. "The limit distribution of the concave majorant of an empirical distribution function." Statistics & Probability Letters 20, no. 1 (1994): 81–84. http://dx.doi.org/10.1016/0167-7152(94)90238-0.

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43

DA FONTOURA COSTA, LUCIANO, and GONZALO TRAVIESO. "STRENGTH DISTRIBUTION IN DERIVATIVE NETWORKS." International Journal of Modern Physics C 16, no. 07 (2005): 1097–105. http://dx.doi.org/10.1142/s0129183105007765.

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This article describes a complex network model whose weights are proportional to the difference between uniformly distributed "fitness" values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e., the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent γ<1 if the fitness has an upper limit and γ>1 if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.

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44

Cavaliere, Giuseppe, and Iliyan Georgiev. "Inference Under Random Limit Bootstrap Measures." Econometrica 88, no. 6 (2020): 2547–74. http://dx.doi.org/10.3982/ecta16557.

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Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the uncon

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45

Laurinčikas, A., and G. Misevičius. "On limit distribution of the Riemann zeta-function." Acta Arithmetica 76, no. 4 (1996): 317–34. http://dx.doi.org/10.4064/aa-76-4-317-334.

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46

Laurinčikas, A. "On limit distribution of the Matsumoto zeta-function." Acta Arithmetica 79, no. 1 (1997): 31–39. http://dx.doi.org/10.4064/aa-79-1-31-39.

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47

Takada, Yoshikazu. "Prediction limit for observation from the exponential distribution." Canadian Journal of Statistics 13, no. 4 (1985): 325–30. http://dx.doi.org/10.2307/3314955.

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48

Aguech, Rafik, Nabil Lasmar, and Hosam Mahmoud. "Limit distribution of distances in biased random tries." Journal of Applied Probability 43, no. 02 (2006): 377–90. http://dx.doi.org/10.1017/s0021900200001704.

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Thetrieis a sort of digital tree. Ideally, to achieve balance, the trie should grow from an unbiased source generating keys of bits with equal likelihoods. In practice, the lack of bias is not always guaranteed. We investigate the distance between randomly selected pairs of nodes among the keys in a biased trie. This research complements that of Christophi and Mahmoud (2005); however, the results and some of the methodology are strikingly different. Analytical techniques are still useful for moments calculation. Both mean and variance are of polynomial order. It is demonstrated that the standa

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49

Yurachkivsky, Andriy. "Limit Distribution of a Generalized Ornstein -- Uhlenbeck Process." International Journal of Statistics and Probability 6, no. 1 (2016): 24. http://dx.doi.org/10.5539/ijsp.v6n1p24.

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Let an $\bR^d$-valued random process $\xi$ be the solution of an equation of the kind $\xi(t)=\xi(0)+\int_0^tA(u)\xi(u)\rd\iota(u)+S(t),$ where $\xi(0)$ is a random variable measurable w.\,r.\,t. some $\sigma$-algebra $\cF(0)$, $S$ is a random process with $\cF(0)$-conditionally independent increments, $\iota$ is a continuous numeral random process of locally bounded variation, and $A$ is a matrix-valued random process such that for any $t>0$ $\int_0^t\|A(s)\|\ |\rd\iota(s)|<\iy.$ Conditions guaranteing existence of the limiting, as $t\to\iy$, distribution of $\xi(t)$ are found. The char

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50

Drezner, Zvi. "On the Limit of the Generalized Binomial Distribution." Communications in Statistics: Theory and Methods 35, no. 2 (2006): 209–21. http://dx.doi.org/10.1080/03610920500439950.

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