Volume 3, Issue 1 (2016)
Random convolution of inhomogeneous dist ...
Modern Stochastics: Theory and Applications
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Random convolution of inhomogeneous distributions with O-exponential tail
Volume 3, Issue 1 (2016), pp. 79–94
Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys
https://doi.org/10.15559/16-VMSTA52
Pub. online: 4 April 2016 Type: Research Article Open Access
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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Heavy tail exponential tail O-exponential tail random sum random convolution inhomogeneous distributions closure property
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