Random convolution of inhomogeneous distributions with -exponential tail
Volume 3, Issue 1 (2016), pp. 79–94
Pub. online: 4 April 2016
Type: Research Article
Open Access
Open Access
Received
28 January 2016
28 January 2016
Revised
21 March 2016
21 March 2016
Accepted
21 March 2016
21 March 2016
Published
4 April 2016
4 April 2016
Abstract
Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables (not necessarily identically distributed), and η be a counting random variable independent of this sequence. We obtain sufficient conditions on $\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of the random sum $S_{\eta }=\xi _{1}+\xi _{2}+\cdots +\xi _{\eta }$ belongs to the class of $\mathcal{O}$-exponential distributions.
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