Local theorems for the Markov binomial distribution
The Markov binomial distribution was considered by many authors [cf. \textit{R. L. Dobrushin}, Izv. Akad. Nauk SSSR, Ser. Mat. 17, 291--330 (1953; Zbl 0052.14301); \textit{J. Gani}, J. Appl. Probab., Spec. Vol. 19A, 321--326 (1982; Zbl 0488.60074); \textit{B. O. Koopman}, Proc. Natl. Acad. Sci. USA 36, 202--207 (1950; Zbl 0037.08502); \textit{R. J. Serfling}, Ann. Probab. 3, 726--731 (1975; Zbl 0321.60018); \textit{Y. H. Wang}, J. Appl. Probab. 18, 937--942 (1981; Zbl 0475.60050) and references therein]. Usually, the limit Poisson or compound Poisson laws were examined. The authors [Stochastic Processes Appl. 82, No. 2, 205--227 (1999; Zbl 0997.60073)] applied some signed compound Poisson approximations. In this paper local estimates for infinitely divisible approximations are studied. Considering the Markov binomial distribution the authors study the accuracy of infinitely divisible approximations. A local version of the Kolmogorov first uniform theorem is obtained. Possible approximations in total variation are discussed. The references contain ten bibliographical hints.
scientific article; zbMATH DE number 1912581