Abstract
As the order statistics of the power Poisson process \(\mathcal {E}_{+}\) diverge to infinity, their sum diverges. On the other hand, as the order statistics of the power Poisson process \(\mathcal {E}_{-}\) converge to zero, their sum may converge. In this chapter, we explore sums induced by the power Poisson process \(\mathcal {E}_{-}\). As we shall see, this sum analysis will give rise to two Lévy-stable laws: one-sided and symmetric.
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Eliazar, I. (2020). Sums. In: Power Laws. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-33235-8_11
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DOI: https://doi.org/10.1007/978-3-030-33235-8_11
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