[1] Bevrani, H., Bening, V. E., Korolev, V. Yu.: 
On the accuracy of approximation of the negative-binomial distribution by the gamma distribution and convergence rate of the distributions of some statistics to the Student distribution. J. Math. Sci. 205 (2015), 1, 34-44. 
DOI 10.1007/s10958-015-2227-6 | 
MR 3403276 
[4] Butzer, P. L., Hahn, L.: 
General theorems on rates of convergence in distribution of random variables I. General limit theorems. J. Multivariate Anal. 8 (1978), 181-201. 
DOI 10.1016/0047-259x(78)90071-4 | 
MR 0497594 
[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. 
MR 0940946 
[6] Gavrilenko, S. V., Zubov, V. N., Korolev, V. Yu.: 
The rate of convergence of the distributions of regular statistics constructed from samples with negatively binomially distributed random sizes to the student distribution. J. Math. Sci. 220 (2017), 6, 701-713. 
DOI 10.1007/s10958-016-3213-3 | 
MR 3595558 
[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. 
MR 2125120 | 
Zbl 1267.60001 
[9] Hogg, R. V., McKean, J. W., Craig, A. T.: 
Introduction to Mathematical Statistics. Seventh edition. Pearson Education, Inc. 2013. 
MR 0137186 
[10] Hung, T. L.: 
On a Probability metric based on Trotter operator. Vietnam J. Math. 35 (2007), 1, 22-33. 
MR 2317431 
[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. 
MR 1471479 
[13] Kirschfink, H.: 
The generalized Trotter operator and weak convergence of dependent random variables in different probability metrics. Results Math. 15 (1989), 294-323. 
DOI 10.1007/BF03322619 | 
MR 0997067 
[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. 
MR 1404685 
[15] Kruglov, V. M., Korolev, V. Yu.: 
Limit theorems for Random Sums (in Russian). Moskov. Gos. Univ., Moscow 1990. 
MR 1072999 
[16] Malinowski, M. T.: 
Geometrically strictly semi-stable law as the limit laws. Discuss. Math. Probab. Statist. 27 (2007), 79-97. 
DOI 10.7151/dmps.1089 | 
MR 2414775 
[17] Peköz, E., Röllin, A.: 
New rates for exponential approximation and the theorems of Rényi and Yaglom. Ann. Probab. 39 (2011), 2, 587-608. 
DOI 10.1214/10-aop559 | 
MR 2789507 
[18] Peköz, E., Röllin, A., Ross, N.: 
Generalized Gamma approximation with rates for urns, walks and trees. Ann. Probab. 44 (2016) 3, 1776-1816. 
DOI 10.1214/15-aop1010 | 
MR 3502594 
[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. 
MR 0315747