The distribution of the number of monotone tuples in the sequence of independent uniformly distributed random variables taking values in the set {0,..., N - 1} is considered. By means of the Stein method, an estimate for the variation distance between the distribution of the number of monotone tuples and compound Poisson distribution are constructed. As a corollary of this result, the limit theorem for the number of monotone tuples is proved. The approximating distribution in it is the distribution of the sum of Poisson number of independent random variables with geometric distribution.
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- Title Compound poisson approximation for the distribution of the number of monotone tuples in random sequence
- Headline Compound poisson approximation for the distribution of the number of monotone tuples in random sequence
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 7 (Приложение)
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Keywords
Stein method, compound Poisson distribution, estimate for the variation distance of the compound Poisson approximation, monotone tuples, метод Стейна, сложное пуассоновское распределение, оценка расстояния по вариации сложной пуассоновской аппроксимации, монотонные цепочкиAuthors
References
Barbour A. D., Chen L. H. Y., and Loh W.-L. Compound Poisson approximation for nonnegative random variables via Stein's method // Ann. Appl. Probab. 1992. V. 20. No. 4. P. 1843-1866.
Roos V. Stein's method for compound Poisson approximation: The local approach // Ann. Appl. Probab. 1994. V. 4. No. 4. P. 1177-1187.
Меженная Н. М. Многомерная нормальная теорема для числа монотонных серий заданной длины в равновероятной случайной последовательности // Обозрение прикладной и промышленной математики. 2007. Т. 14. Вып.3. С. 503-505.
Pittel B. G. Limiting behavior of a process of runs // Ann. Probab. 1981. V. 9. No. 1. P. 119-129.
Chryssaphinou O., Papastavridis S., and Vaggelatou E. Poisson approximation for the non-overlapping appearances of several words in Markov chains // Combinatorics, Probability and Computing. 2001. V. 10. No. 4. P. 293-308.
David F. N. and Barton D. E. Combinatorial Chance. Hafner Publishing Co., New York, 1962.
Wolfowitz J. Asymptotics distribution of runs up and down // Ann. Math. Statist. 1944. V. 15. P. 163-172.
Compound poisson approximation for the distribution of the number of monotone tuples in random sequence | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).
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