Normal and degenerate convergences of random sums

1989 ◽  
pp. 124-136
Author(s):  
V. M. Kruglov
Keyword(s):  
Random Sums

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

Convolution equivalence and distributions of random sums

2007 ◽  
Vol 142 (3-4) ◽  
pp. 367-397 ◽  
Author(s):  
Toshiro Watanabe
Keyword(s):  
Random Sums

o-Rates of closeness of two weighted random sums of dependent banach-valued random variables

1986 ◽  
Vol 25 (2) ◽  
pp. 119-127
Author(s):  
Paul L. Butzer ◽  
Dietmar Schulz
Keyword(s):  
Random Variables ◽  
Random Sums

Random sums

Risk Theory ◽  
2017 ◽  
pp. 169-229
Keyword(s):  
Random Sums

Limit theorems for random sums in the double array scheme

2020 ◽  
pp. 93-152
Author(s):  
Boris V. Gnedenko ◽  
Victor Yu. Korolev
Keyword(s):  
Limit Theorems ◽  
Random Sums ◽  
Double Array ◽  
Array Scheme

scholarly journals Asymptotics of weighted random sums

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
José Manuel Corcuera ◽  
David Nualart Nualart ◽  
Mark Podolskij
Keyword(s):  
Random Sums
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