Results 11 to 20 of about 233 (153)
Berry-Esséen bound of sample quantiles for negatively associated sequence
Journal of Inequalities and Applications, 2011 In this paper, we investigate the Berry-Esséen bound of the sample quantiles for the negatively associated random variables under some weak conditions. The rate of normal approximation is shown as O(n -1/9). 2010 Mathematics Subject Classification:
Zhang Qinchi +3 more
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ON RANDOM CONVEX CHAINS, ORTHOGONAL POLYNOMIALS, PF SEQUENCES AND PROBABILISTIC LIMIT THEOREMS
Mathematika, Volume 67, Issue 2, Page 434-446, April 2021., 2021 Abstract Let T be the triangle in the plane with vertices (0,0), (0,1) and (0,1). The convex hull of (0,1), (1,0) and n independent random points uniformly distributed in T is the random convex chain Tn. A three‐term recursion for the probability generating function Gn of the number f0(Tn) of vertices of Tn is proved.
Anna Gusakova, Christoph Thäle
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A semicircle law and decorrelation phenomena for iterated Kolmogorov loops
Journal of the London Mathematical Society, Volume 103, Issue 2, Page 558-586, March 2021., 2021 Abstract We consider a standard one‐dimensional Brownian motion on the time interval [0,1] conditioned to have vanishing iterated time integrals up to order N. We show that the resulting processes can be expressed explicitly in terms of shifted Legendre polynomials and the original Brownian motion, and we use these representations to prove that the ...
Karen Habermann
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Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 66, Page 3565-3576, 2004., 2004 Let {X, Xn; n ≥ 1} be a sequence of real‐valued i.i.d. random variables and let Sn=∑i=1nXi, n ≥ 1. In this paper, we study the probabilities of large deviations of the form P(Sn > tn1/p), P(Sn < −tn1/p), and P(|Sn| > tn1/p), where t > 0 and 0 < p < 2.
Deli Li, Andrew Rosalsky
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On multiple‐particle continuous‐time random walks
Journal of Applied Mathematics, Volume 2004, Issue 3, Page 213-233, 2004., 2004 Scaling limits of continuous‐time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous‐time random walk.
Peter Becker-Kern, Hans-Peter Scheffler
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Cauchy approximation for sums of independent random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 17, Page 1055-1066, 2003., 2003 We use Stein′s method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.
K. Neammanee
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A zero‐inflated occupancy distribution: exact results and Poisson convergence
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 28, Page 1771-1782, 2003., 2003 We introduce the generalized zero‐inflated allocation scheme of placing n labeled balls into N labeled cells. We study the asymptotic behavior of the number of empty cells when (n, N) belongs to the “right” and “left” domain of attraction. An application to the estimation of characteristics of agreement among a set of raters which independently ...
Nikolai Kolev, Ljuben Mutafchiev
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A nonuniform bound for the approximation of Poisson binomial by Poisson distribution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 48, Page 3041-3046, 2003., 2003 It is well known that Poisson binomial distribution can be approximated by Poisson distribution. In this paper, we give a nonuniform bound of this approximation by using Stein‐Chen method.
K. Neammanee
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A survey of limit laws for bootstrapped sums
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 45, Page 2835-2861, 2003., 2003 Concentrating mainly on independent and identically distributed (i.i.d.) real‐valued parent sequences, we give an overview of first‐order limit theorems available for bootstrapped sample sums for Efron′s bootstrap. As a light unifying theme, we expose by elementary means the relationship between corresponding conditional and unconditional bootstrap ...
Sándor Csörgő, Andrew Rosalsky
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Open Mathematics, 2017 Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’
Dudziński Marcin, Furmańczyk Konrad
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