On a generalization of class of negative binomial distributions
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Alexander N. Timashev
Abstract
A class of one-dimensional discrete power series distributions containing negative binomial distributions is considered. Properties of distributions of this class are investigated. Limit theorems generalizing similar theorems for the negative binomial distributions are proved. The proofs are based both on elementary asymptotic methods and on a modification of saddle-point method.
Note
Originally published in Diskretnaya Matematika (2021) 33,№1, 64–81 (in Russian).
References
[1] Ivchenko G.I., Medvedev Yu.I., Discrete Distributions. Probabilistic-Statictical Handbook. One-Dimensional Distributions, Moscow, Lenand, 2014 (in Russian), 256 pp.Search in Google Scholar
[2] Bender E. A., “Asymptotic methods in enumeration”, SIAM Review, 16:4 (1974), 485–515.10.1137/1016082Search in Google Scholar
[3] Szegö G., Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ., XXIII, rev. ed., Amer. Math. Soc., N.-Y., 1959.Search in Google Scholar
[4] Timashev A.N., Distributions of the Power Series Type and the Generalized Allocation Scheme, Moscow: izd. dom «Academia», 2017 (In Russian), 168 pp.Search in Google Scholar
[5] Copson E. T., Asymptotic Expansions, Cambridge Univ. Press, 1965.10.1017/CBO9780511526121Search in Google Scholar
[6] Olver F. W. J., Introduction to Asymptotics and Special Functions, Academic Press, 1974, 312 pp.10.1016/B978-0-12-525856-2.50005-XSearch in Google Scholar
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Articles in the same Issue
- Contents
- Group service system with three queues and load balancing
- Formulas for the numbers of sequences containing a given pattern given number of times
- On a generalization of class of negative binomial distributions
- Invertible matrices over some quotient rings: identification, generation, and analysis
- On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs
- Computation of distributions of statistics by means of Markov chains
Articles in the same Issue
- Contents
- Group service system with three queues and load balancing
- Formulas for the numbers of sequences containing a given pattern given number of times
- On a generalization of class of negative binomial distributions
- Invertible matrices over some quotient rings: identification, generation, and analysis
- On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs
- Computation of distributions of statistics by means of Markov chains
