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Normal approximation under local dependence [PDF]
The Annals of Probability, 2004 We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible.
Louis H. Y. Chen, No. A, Qi-man Shao
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Error bounds in stochastic-geometric normal approximation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We provide normal approximation error bounds for sums of the form $\sum_x \xi_x$, indexed by the points $x$ of a Poisson process (not necessarily homogeneous) in the unit $d$-cube, with each term $\xi_x$ determined by the configuration of Poisson points ...
Mathew Penrose, Tom Rosoman
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Nonlinear quasi-normal modes: uniform approximation
Journal of High Energy Physics, 2023 Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown.
Bruno Bucciotti +3 more
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Discretized normal approximation by Stein's method
Bernoulli, 2014 We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution.
Fang, Xiao
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Approximate skew normal distribution
Journal of Advanced Research, 2010 We propose a new approximate skew normal distribution, it is easy to calculate, convenient, mathematically tractable and is in a closed form. It is particularly useful when the probability density function occurs in an expression to be used for further ...
Samir K. Ashour, Mahmood A. Abdel-hameed
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Approximations of normal distribution by its q-generalizations [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 A concept of q-generalization of normal distribution arises in the context of statistical mechanics. In this article, we introduce a q-generalization of normal approximation.
Mongkhon Tuntapthai
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Asymptotically Exact Constants in Natural Convergence Rate Estimates in the Lindeberg Theorem
Mathematics, 2021 Following (Shevtsova, 2013) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limit theorem, namely in Esseen’s, Rozovskii’s, and Wang–Ahmad’s inequalities ...
Ruslan Gabdullin +2 more
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On the normal approximation for weakly dependent random variables
Lietuvos Matematikos Rinkinys, 2005 In this report, we present the estimates of the difference |Eh(Zn) − Eh(N)|, where Zn is a sum of n centered and normalized random variables which satisfy the strong mixing condition (without assuming a stationarity), and N is a standard normal random ...
Jonas Sunklodas
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New Journal of Physics, 2021 The paper (Hayashi M and Tsurumaru T 2012 New J. Phys. https://doi.org/10.1088/1367-2630/14/9/093014 https://doi.org/10.1088/1367-2630/14/9/093014 ) contains an error at the definition of g _t ( x ) in section 5.3 while g _t ( x ) is used for the second ...
Masahito Hayashi, Toyohiro Tsurumaru
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Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions
Mathematics, 2022 In this paper, we study the inferences of the difference of medians for two independent log-normal distributions. These methods include traditional methods such as the parametric bootstrap approach, the normal approximation approach, the method of ...
Weizhong Tian +2 more
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