On Convergence of Random Sums of Random Variables to the Normal Law

1974 ◽  
Vol 18 (2) ◽  
pp. 366-367 ◽  
Author(s):  
A. V. Pechinkin
Keyword(s):  
Random Variables ◽  
Random Sums ◽  
Sums Of Random Variables ◽  
Normal Law

Random Sums of Random Variables as Economic Processes: Sales

1967 ◽  
Vol 4 (3) ◽  
pp. 296-302 ◽  
Author(s):  
Haskel Benishay
Keyword(s):  
Stock Prices ◽  
Random Variables ◽  
Random Sums ◽  
Sums Of Random Variables

The cumulation of a sum of N observations from a distribution of Y where N and Y are linearly related random variables may serve as a model for the description of sales, insurance payments, changes in stock prices and other economic processes. The expectation and variance of such a sum and other results are presented with an empirical example. This model may prove useful for description of various flow magnitudes per interval of time that are, in turn, random cumulations of random outcomes.

Poisson and compound Poisson approximations for random sums of random variables

1996 ◽  
Vol 33 (01) ◽  
pp. 127-137 ◽  
Author(s):  
P. Vellaisamy ◽  
B. Chaudhuri
Keyword(s):  
Lower Bound ◽  
Total Variation ◽  
Random Variables ◽  
Upper Bounds ◽  
Random Sums ◽  
Compound Poisson ◽  
Sums Of Random Variables ◽  
Variation Distance ◽  
Poisson Approximations ◽  
Better Than

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.

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