Abstract
Besides the convolution closure, it is often of interest to understand whether the attribution of a distribution F to the specific class of distributions is caused by the inclusion of \(F^{*n}\) to the same family. Such an implication is called a convolution-root closure. This chapter is devoted to the convolution-root closure properties for the distribution classes described in Chap. 2. We determine the classes which are closed under convolution roots and which are not.
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Notes
- 1.
If an infinitely divisible distribution belonging to a certain distribution class implies that its Lévy distribution also belongs to the same class, then the class is said to be closed under infinitely divisible distribution roots (see Xu et al. [202]).
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Leipus, R., Šiaulys, J., Konstantinides, D. (2023). Convolution-Root Closure. In: Closure Properties for Heavy-Tailed and Related Distributions. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-34553-1_4
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DOI: https://doi.org/10.1007/978-3-031-34553-1_4
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