Abstract
AbstractOne of the most fundamental probabilities is the probability at a particular point. The local limit theorem is the well-known theorem that estimates this probability. In this paper, we estimate this probability by the density function of normal distribution in the case of lattice integer-valued random variables. Our technique is the characteristic function method. We complete to relax the third moment condition of Siripraparat and Neammanee (J. Inequal. Appl. 2021:57, 2021) and the references therein and also obtain explicit constants of the error bound.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference19 articles.
1. Siripraparat, T., Neammanee, K.: An improvement of convergence rate in the local limit theorem for integral-valued random variables. J. Inequal. Appl. 2021, 57, 1–18 (2021)
2. Siripraparat, T., Neammanee, K.: A local limit theorem for Poisson binomial random variables. ScienceAsia 47, 111–116 (2021)
3. Doob, J.L.: Stochastic Processes. Wiley, New York (1953)
4. Prokhorov, Y.V., Rozanov, Y.A.: Probability Theory [in Russian]. Nauka, Moscow (1973)
5. Statulyavichus, V.A.: Limit theorems for densities and asymptotic decompositions for distributions of sums of independent random variables. Theory Probab. Appl. 10(4), 582–595 (1965)
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