On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution

Tran Loc Hung; Tran Ngoc Hau

Kybernetika (2018)

  • Volume: 54, Issue: 5, page 921-936
  • ISSN: 0023-5954

Abstract

top
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.

How to cite

top

Hung, Tran Loc, and Hau, Tran Ngoc. "On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution." Kybernetika 54.5 (2018): 921-936. <http://eudml.org/doc/294248>.

@article{Hung2018,
abstract = {The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.},
author = {Hung, Tran Loc, Hau, Tran Ngoc},
journal = {Kybernetika},
keywords = {gamma distribution; negative-binomial random sums; Trotter's distance},
language = {eng},
number = {5},
pages = {921-936},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution},
url = {http://eudml.org/doc/294248},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Hung, Tran Loc
AU - Hau, Tran Ngoc
TI - On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 5
SP - 921
EP - 936
AB - The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
LA - eng
KW - gamma distribution; negative-binomial random sums; Trotter's distance
UR - http://eudml.org/doc/294248
ER -

References

top
  1. Bevrani, H., Bening, V. E., Korolev, V. Yu., 10.1007/s10958-015-2227-6, J. Math. Sci. 205 (2015), 1, 34-44. MR3403276DOI10.1007/s10958-015-2227-6
  2. Brown, M., 10.1214/aop/1176990750, Ann. Probab. 18 (1990), 3, 1388-1402. MR1062073DOI10.1214/aop/1176990750
  3. Butzer, P. L., Hahn, L., U., Westphal, 10.1016/0021-9045(75)90042-8, J. Approx. Theory 13 (1975), 327-340. MR0394809DOI10.1016/0021-9045(75)90042-8
  4. Butzer, P. L., Hahn, L., 10.1016/0047-259x(78)90071-4, J. Multivariate Anal. 8 (1978), 181-201. MR0497594DOI10.1016/0047-259x(78)90071-4
  5. Butzer, P. L., Kirschfink, H., Schulz, D., An extension of the Lindeberg-Trotter operator-theoretic approach to limit theorems for dependent random variables., Acta Sci. Math. 51 (1987), 423-433. MR0940946
  6. Gavrilenko, S. V., Zubov, V. N., Korolev, V. Yu., 10.1007/s10958-016-3213-3, J. Math. Sci. 220 (2017), 6, 701-713. MR3595558DOI10.1007/s10958-016-3213-3
  7. Grandell, J., Risk Theory and geometric sums., Inform. Processes 2 (2002) 2, 180-181. 
  8. Gut, A., Probability: A Graduate Course., Springer Texts in Statistics. Springer, New York 2005. Zbl1267.60001MR2125120
  9. Hogg, R. V., McKean, J. W., Craig, A. T., Introduction to Mathematical Statistics. Seventh edition., Pearson Education, Inc. 2013. MR0137186
  10. Hung, T. L., On a Probability metric based on Trotter operator., Vietnam J. Math. 35 (2007), 1, 22-33. MR2317431
  11. Hung, T. L., On the rate of convergence in limit theorems for geometric sums., Southeast Asian J. Sci. 2 (2013) 2, 117-130. 
  12. Kalashnikov, V., Geometric Sums: Bounds for Rare Events with Applications., Kluwer Academic Publisher 1997. MR1471479
  13. Kirschfink, H., 10.1007/BF03322619, Results Math. 15 (1989), 294-323. MR0997067DOI10.1007/BF03322619
  14. Korolev, V. Yu., Convergence of random sequences with independent random indices. I (in Russian)., Teor. Veroyatnost. i Primenen. 39 (1994), 2, 313-333; translation in Theory Probab. Appl. 39 (1995), 2, 282-297. MR1404685
  15. Kruglov, V. M., Korolev, V. Yu., Limit theorems for Random Sums (in Russian)., Moskov. Gos. Univ., Moscow 1990. MR1072999
  16. Malinowski, M. T., 10.7151/dmps.1089, Discuss. Math. Probab. Statist. 27 (2007), 79-97. MR2414775DOI10.7151/dmps.1089
  17. Peköz, E., Röllin, A., 10.1214/10-aop559, Ann. Probab. 39 (2011), 2, 587-608. MR2789507DOI10.1214/10-aop559
  18. Peköz, E., Röllin, A., Ross, N., 10.1214/15-aop1010, Ann. Probab. 44 (2016) 3, 1776-1816. MR3502594DOI10.1214/15-aop1010
  19. Rényi, A., Probability Theory., North-Holland Series in Applied Mathematics and Mechanics 10, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York. 1970. MR0315747
  20. Rychlick, Z., 10.4064/cm-35-1-147-158, Coll. Math. 35 (1976), 147-158. MR0410866DOI10.4064/cm-35-1-147-158
  21. Sunklodas, J. K., 10.1007/s10986-015-9271-2, Lith. Math. J. 55 (2015), 1, 150-158. MR3323288DOI10.1007/s10986-015-9271-2
  22. Trotter, H. F., 10.1007/BF01240790, Arch. Math. 10 (1959), 226-234. MR0108847DOI10.1007/BF01240790

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.