Lower Bounds for Discrete Approximations to Sums of m-Dependent Random Variables

• Autorzy: Čekanavičius Vydas , Vellaisamy Palaniappan

Identyfikatory

DOI

10.37190/0208-4147.40.1.2

• Języki publikacji: EN

Abstrakty

EN

Lower bounds for the second order Poisson, compound Poisson, negative binomial and binomial approximations to the sum of 1-dependent random variables are obtained for the Kolmogorov and local metrics. The results are then applied to sums of independent indicators and runs statistics.

Słowa kluczowe

EN

Poisson approximation; signed compound Poisson measure; binomial approximations; negative binomial approximations; one-dependent variables; local norm; Kolmogorov distance

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 1
• Strony: 23--35
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Čekanavičius Vydas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 03225, Lithuania

autor

Vellaisamy Palaniappan

• Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

Bibliografia

• [1] A. D. Barbour and V. Čekanavičius, Total variation asymptotics for sums of independent integer random variables, Ann. Probab. 30 (2002), 509-545.
• [2] A. D. Barbour, L. Holst and S. Janson, Poisson Approximation, Clarendon Press, Oxford, 1992.
• [3] V. Čekanavičius, Approximation Methods in Probability Theory, Universitext, Springer, 2016.
• [4] V. Čekanavičius and B. Roos, Two-parametric compound binomial approximations, Lithuanian Math. J. 44 (2004), 354-373.
• [5] V. Čekanavičius and P. Vellaisamy, Discrete approximations for sums of m-dependent random variables, ALEA Latin Amer. J. Probab. Math. Statist. 12 (2015), 765-792.
• [6] W. T. Huang and C. S. Tsai, On a modified binomial distribution of order k, Statist. Probab. Lett. 11 (1991), 125-131.
• [7] J. Kruopis, Precision of approximation of the generalized binomial distribution by convolutions of Poisson measures, Lithuanian Math. J. 26 (1986), 37-49.
• [8] B. Roos, Poisson approximation via the convolution with Kornya-Presman signed measures, Theory Probab. Appl. 48 (2004), 555-560.
• [9] S. Y. T. Soon, Binomial approximation for dependent indicators, Statist. Sinica 6 (1996), 703-714.
• [10] P. Vellaisamy, Poisson approximation for (k1, k2) events via the Stein-Chen method, J. Appl. Probab. 41 (2004), 1081-1092.
• [11] X. Wang and A. Xia, On negative binomial approximation to k-runs, J. Appl. Probab. 45 (2008), 456-471.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).