Studies on generalized Yule models

Abstract

We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.

Published at https://doi.org/10.15559/18-VMSTA125 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

References in corpus (4)

• The Prabhakar or three parameter Mittag--Leffler function: theory and application
• A fractional generalization of the Poisson processes
• Scale-free behavior of networks with the copresence of preferential and uniform attachment rules
• The dynamics of power laws: Fitness and aging in preferential attachment trees

Cited by in corpus (1)

• A practical guide to Prabhakar fractional calculus