An improvement of convergence rate in the local limit theorem for integral-valued random variables

DOI10.1186/s13660-021-02590-2zbMath1504.60038OpenAlexW3164254036MaRDI QIDQ2072818

Tatpon Siripraparat, K. Neammanee

Publication date: 26 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-021-02590-2

zbMATH Keywords

convergence ratelocal limit theoremlattice random variablenormal density function

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05)

Related Items (2)

Local limit theorems without assuming finite third moment ⋮ Local limit theorems for collective risk models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An improvement of convergence rate estimates in the Lyapunov theorem
• Refinement of the upper bound of the constant in the central limit theorem
• An estimate of the modulus of the characteristic function of a lattice distribution with application to remainder term estimates in local limit theorems
• Lower and upper bounds for characteristic functions
• Approximate local limit theorems with effective rate and application to random walks in random scenery
• On a bound of the absolute constant in the Berry-Esseen inequality for i.i.d. Bernoulli random variables
• A refinement of normal approximation to Poisson binomial
• Moment-Type Estimates with an Improved Structure for the Accuracy of the Normal Approximation to Distributions of Sums of Independent Symmetric Random Variables
• An upper bound for characteristic functions of lattice distributions with applications to survival probabilities of quantum states
• A non uniform bound for half-normal approximation of the number of returns to the origin of symmetric simple random walk
• Bounds for Characteristic Functions and Laplace Transforms of Probability Distributions
• A Refinement of the Remainder in the Lyapunov Theorem
• Selected Topics in Characteristic Functions
• Limit Theorems for Densities and Asymptotic Expansions for Distributions of Sums of Independent Random Variables
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates

This page was built for publication: An improvement of convergence rate in the local limit theorem for integral-valued random variables