1 |
J. Melamed, Limit theorems in the set-up of summation of a random number of independent identically distributed random variables, Lecture Notes in Math., Vol. 1412, Springer, Berlin, (1989), 194–228.
DOI
|
2 |
J. Modyorodi, A central limit theorem for the sums of a random number of random variables, Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 10 (1967), 171–182.
|
3 |
H. Robbins, The asymptotic distribution of the sum of a random number of random variables, Bull. Amer. Math. Soc. 54 (1948), 1151–1161.
DOI
|
4 |
W. Feller, An Introduction to Probability Theory and Its Applications, volume II, 2nd edition, John Wiley & Sons, New York, 1971.
|
5 |
B. Gnedenko, Limit theorems for sums of a random number of positive independent random variables, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, Univ. California Press, Berkeley, Calif. (1972), 537–549.
|
6 |
B. Gnedenko, On limit theorems for a random number of random variables, Probability theory and mathematical statistics (Tbilisi, 1982), Lecture Notes in Math., 1021 Springer, Berlin, (1983), 167–176.
DOI
|
7 |
A. Krajka, Z. Rychlik, Necessary and sufficient conditions for weak convergence of random sums of independent random variables, Comment. Math. Univ. Carolinae 34 (1993), no. 3, 465–482.
|
8 |
V. Kruglov and V. Korolev, Limit Theorems for Random Sums, Moscow University Press, Moscow, 1990.
|
9 |
Z. Rychlik and T. Walczynski, Convergence in law of random sums with nonrandom centering, J. Math. Sci. (New York) 106 (2001), 2860–2864.
DOI
|
10 |
Z. Rychlik and D. Szynal, On the limit behaviour of sums of a random number of independent random variables, Colloq. Math. 28 (1973), 147–159.
DOI
|
11 |
D. O. Selivanova, Estimates for the rate of convergence in some limit theorems for geometric random sums, Moscow Univ. Comput. Math. Cybernet. (1995), no. 2, 27–31.
|
12 |
Yu. B. Shvetlov and John J. Borkowski, Random sum estimators and their efficiency, Technical Report, Department of Mathematical Science, Montana State University, (2004), 1–20.
|
13 |
D. Szasz, Limit theorems for the distributions of the sums of a random number of random variables, Ann. Math. Statist. 43 (1972), 1902–1913.
DOI
|
14 |
P. Vellaisamy and B. Chaudhuri, Poisson and compound Poisson approximations for random sums of random variables, J. Appl. Probab. 33 (1996), 127–137.
DOI
ScienceOn
|