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On the Accuracy of Normal Approximation for the Densities of Sums of Independent Identically Distributed Random Variables

Theory of Probability & Its Applications, 2000
Summary: The structure of the nonuniform estimate of the convergence rate in the local central limit theorem for the densities of sums of independent identically distributed random variables is made more accurate. The absolute constants are written out explicitly.
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On approximation and estimation of distribution function of sum of independent random variables

Statistical Papers, 2023
N. N. Midhu   +3 more
semanticscholar   +1 more source

Density Function of Weighted Sum of Chi-Square Variables with Doubly Degenerate Weights

Optical Memory and Neural Networks, 2022
B. Kryzhanovsky, V. I. Egorov
semanticscholar   +1 more source

Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables

Lithuanian Mathematical Journal, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Center, Scale and Asymptotic Normality for Censored Sums of Independent, Nonidentically Distributed Random Variables

1991
This paper develops a new approach (called the Censored Centered Method, or CCM) to the problem of determining centers and scales for distributions, and features applications to asymptotic normality for censored sums of independent, generally nonidentically distributed random variables.
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Estimates of the Distance Between the Distribution of a Sum of Independent Random Variables and the Normal Distribution

1975
The results of this section, which are of interest in themselves, will play an important role in Chapters V and VI.
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Moment-Type Estimates with an Improved Structure for the Accuracy of the Normal Approximation to Distributions of Sums of Independent Symmetric Random Variables

Theory of Probability & Its Applications, 2013
For the uniform distance $\Delta_n$ between the distribution function of the standard normal law and the distribution function of the normalized sum of $n$ independent random variables $X_1,\ldots,X_n$ with symmetric distribution functions $F_1,\ldots,F_n$ and ${\mathbf E}\,|X_j|=\beta_{1,j}$, ${\mathbf E}\,X_j^2=\sigma_j^2$, ${j=1,\ldots,n}$, for all $
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