Geodesic
Local limit theorems for compound discrete distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 589-600 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Local limit theorems for compound discrete distributions (a normal theorem and a large deviation theorem) are put forward. Some examples of such distributions, including compound Poisson, compound binomial, and negative binomial distributions, are considered. Our analysis is based on elementary asymptotic methods in combination with the saddle-point method.
Keywords: local limit theorems, compound discrete distributions, compound Poisson distribution, large deviations, saddle-point method.
Mots-clés : binomial distribution, negative binomial distribution 
@article{TVP_2021_66_3_a10,
     author = {A. N. Timashev},
     title = {Local limit theorems for compound discrete distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {589--600},
     year = {2021},
     volume = {66},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a10/}
}
TY  - JOUR
AU  - A. N. Timashev
TI  - Local limit theorems for compound discrete distributions
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 589
EP  - 600
VL  - 66
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a10/
LA  - ru
ID  - TVP_2021_66_3_a10
ER  - 
%0 Journal Article
%A A. N. Timashev
%T Local limit theorems for compound discrete distributions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 589-600
%V 66
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a10/
%G ru
%F TVP_2021_66_3_a10
A. N. Timashev. Local limit theorems for compound discrete distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 589-600. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a10/

[1] V. V. Petrov, Sums of independent random variables, Ergeb. Math. Grenzgeb., 82, Springer-Verlag, New York–Heidelberg, 1975, x+346 pp. | DOI | MR | MR | Zbl | Zbl

[2] A. N. Timashev, Bolshie ukloneniya v veroyatnostnoi kombinatorike, Izd. dom «Akademiya», M., 2011, 248 pp.

[3] G. I. Ivchenko, Yu. I. Medvedev, Diskretnye raspredeleniya. Veroyatnostno-statisticheskii spravochnik. Odnomernye raspredeleniya, Lenand, M., 2015, 256 pp.

[4] N. L. Johnson, S. Kotz, A. W. Kemp, Univariate discrete distributions, Wiley Ser. Probab. Math. Statist. Appl. Probab. Statist., 2nd ed., John Wiley Sons, Inc., New York, 1992, xxii+565 pp. | MR | Zbl

[5] A. N. Timashev, Asimptoticheskie razlozheniya v veroyatnostnoi kombinatorike, TVP, M., 2010, 312 pp.

[6] E. T. Copson, Asymptotic expansions, Cambridge Tracts in Math. and Math. Phys., 55, Cambridge Univ. Press, New York, 1965, vii+120 pp. | DOI | MR | Zbl | Zbl