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Article
On the Randomized Bernstein Approximation Theorem and the Order of Approximation
The Weierstrass Approximation Theorem provides an important result by approximating a given continuous function defined on a closed interval to a polynomial function. The Weierstrass Approximation theorem has ...
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Article
On the Rate of Convergence in Limit Theorems for Negative–Binomial Random Sums
The main purpose of this paper is to study the rate of convergence in limit theorems for normalized negative–binomial random sums of independent, identically distributed random variables. The obtained limit di...
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Article
An Extension of Zolotarev’s Problem and Some Related Results
The main purpose of this paper is to extend the Zolotarev’s problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables. This extensio...
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Article
On the Order of Approximation in Limit Theorems for Negative–Binomial Sums of Strictly Stationary m-Dependent Random Variables
During the last several decades, the results related to geometric random sums of independent identically distributed random variables have become interesting results in probability theory and in insurance, ris...
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Article
On the Rates of Convergence in Central Limit Theorems for Compound Random Sums of Independent Random Variables
Since the appearance of Robbins’s paper (1948) the central limit theorem for a sum of a random number of independent identically distributed random variables is one of the most fundamental results in probabili...
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Article
Correction to: On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of 𝓂-dependent random variables
In the metadata of the article on SpringerLink, the corresponding author is incorrect. The corresponding author is Tran Loc Hung (tlhung@ufm.edu.vn; tlhungvn@gmail.com)
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Article
On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of m-dependent random variables
In this paper, we consider a strictly stationary sequence of m-dependent random variables through a compatible sequence of independent and identically distributed random variables by the moving averages processes...
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Article
Some Results on Approximation for Distributions of Random Sums by Poisson Distribution
The main purpose of this paper is to investigate the bounds in Poisson approximation of the distributions for random sums by Poisson distribution via a probability distance based on linear operator introduced ...
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Article
Open AccessOn bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables
Using the Stein–Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
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Article
Open AccessOn bounds in Poisson approximation for integer-valued independent random variables
The main aim of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent integer-valued random variables via the Trotter-Renyi distance. Some results related to random ...
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Article
Open AccessOn the rate of convergence in limit theorems for random sums via Trotter-distance
The main purpose of this paper is to establish some estimates for the rates of convergence in limit theorems for random sums of independent identically distributed random variables via Trotter-distance.
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Article
Open AccessBounds for the approximation of Poisson-binomial distribution by Poisson distribution
Let ( X n ...
