On the stability of the distribution íunction o f the composed random variables by their index random variable
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Abstract
b s t r a c t . Let us consider the composed random variable TỊ = Y l k = 1 &> vvhere —
are independent iđentically distributed random variables and V is a positivc value random,
independent of all
In [1] and [2], we gave some the stabilities of the distribution function o f 7] in the following
sense: the small changes in the distribution íunction o f Ẹk only lcad to the small changes in
the distribution íunction o f TỊ.
In the paper, we investigate the distribution íunction o f TỊ vvhen we have the small changes of
the distribution of V.
References
Tran Kim Thanh, On the characterization o f the distribưtion o f the composed random variables and their stabilities
Doctor thesis, Hanoi 2000.
|2] Tran Kim Thanh, Nguyên Huu Bao, On the gcomctric composcd variables and thc cstimate of ihe stablc degree of ứic
Renyi's charactcristic theorcm, Acta Mathemaica Vietnamica 21 (1996) 269.
[3] c. G. Esscn, Fouricr analysis of distribution tunctions, Ảcta Math. 77 (1945) 125.
Doctor thesis, Hanoi 2000.
|2] Tran Kim Thanh, Nguyên Huu Bao, On the gcomctric composcd variables and thc cstimate of ihe stablc degree of ứic
Renyi's charactcristic theorcm, Acta Mathemaica Vietnamica 21 (1996) 269.
[3] c. G. Esscn, Fouricr analysis of distribution tunctions, Ảcta Math. 77 (1945) 125.